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Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review
<!doctype html> <html data-n-head-ssr lang="en" data-n-head="%7B%22lang%22:%7B%22ssr%22:%22en%22%7D%7D"> <head > <meta data-n-head="ssr" charset="utf-8"><meta data-n-head="ssr" name="viewport" content="width=device-width,initial-scale=1.0,maximum-scale=1.0, user-scalable=0"><meta data-n-head="ssr" http-equiv="Content-Security-Policy" content="default-src * data:; child-src * 'self' blob: http:;img-src * 'self' data: http:; script-src 'self' 'unsafe-inline' 'unsafe-eval' *;style-src 'self' 'unsafe-inline' *"><meta data-n-head="ssr" name="keywords" content="Distributed model predictive control,autonomous intelligent systems,multi-agent systems,unmanned aerial vehicles,vehicle platoon systems"><meta data-n-head="ssr" name="description" content="This paper reviews the application of distributed model predictive control (DMPC) for autonomous intelligent systems (AIS) with unmanned aerial vehicles (UAVs) and vehicle platoon systems. DMPC is an optimal control method that formulates and solves optimization problems to adjust control strategies by predicting future states based on system models while managing constraints, and this technique has been applied to an increasing number of industrial areas. As the essential parts of AIS, UAVs and vehicle platoon systems have received extensive attention in the civil, industrial, and military fields. DMPC has the ability to quickly solve optimization problems in real-time while taking into account the prediction of the future state of the system, which fits in well with the ability of AIS to predict the environment when making decisions, so the application of DMPC in AIS has a natural advantage. This paper first introduces the basic principles of DMPC and the theoretical results in multi-agent systems (MASs). It then reviews the application of DMPC methods to UAVs and vehicle platoon systems. Finally, the challenges of the existing methods are summarized to offer insights to advance the future development of DMPC in practical applications."><meta data-n-head="ssr" name="dc.title" content="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review"><meta data-n-head="ssr" name="journal_id" content="ir.2024.19"><meta data-n-head="ssr" name="dc.date" content="2024-09-24"><meta data-n-head="ssr" name="dc.identifier" content="doi:10.20517/ir.2024.19"><meta data-n-head="ssr" name="dc.publisher" content="OAE Publishing Inc."><meta data-n-head="ssr" name="dc.type" content="Review"><meta data-n-head="ssr" name="dc.source" content=" Intell Robot 2024;4(3):293-317."><meta data-n-head="ssr" name="dc.citation.spage" content="293"><meta data-n-head="ssr" name="dc.citation.epage" content="317"><meta data-n-head="ssr" name="dc.creator" content="Yang Peng"><meta data-n-head="ssr" name="dc.creator" content="Huaicheng Yan"><meta data-n-head="ssr" name="dc.creator" content="Kai Rao"><meta data-n-head="ssr" name="dc.creator" content="Penghui Yang"><meta data-n-head="ssr" name="dc.creator" content="Yunkai Lv"><meta data-n-head="ssr" name="dc.subject" content="Distributed model predictive control"><meta data-n-head="ssr" name="dc.subject" content="autonomous intelligent systems"><meta data-n-head="ssr" name="dc.subject" content="multi-agent systems"><meta data-n-head="ssr" name="dc.subject" content="unmanned aerial vehicles"><meta data-n-head="ssr" name="dc.subject" content="vehicle platoon systems"><meta data-n-head="ssr" name="citation_reference" content="citation_title=Aceto&nbsp;G, Persico&nbsp;V, Pescapé&nbsp;A. 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IEEE; 2023. pp. 507–14."><meta data-n-head="ssr" name="citation_journal_title" content="Intelligence & Robotics"><meta data-n-head="ssr" name="citation_publisher" content="OAE Publishing Inc."><meta data-n-head="ssr" name="citation_title" content="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review"><meta data-n-head="ssr" name="citation_publication_date" content="2024/09/24"><meta data-n-head="ssr" name="citation_online_date" content="2024/09/24"><meta data-n-head="ssr" name="citation_doi" content="10.20517/ir.2024.19"><meta data-n-head="ssr" name="citation_volume" content="4"><meta data-n-head="ssr" name="citation_issue" content="3"><meta data-n-head="ssr" name="citation_firstpage" content="293"><meta data-n-head="ssr" name="citation_lastpage" content="317"><meta data-n-head="ssr" name="citation_author" content="Yang Peng"><meta data-n-head="ssr" name="citation_author" content="Huaicheng Yan"><meta data-n-head="ssr" name="citation_author" content="Kai Rao"><meta data-n-head="ssr" name="citation_author" content="Penghui Yang"><meta data-n-head="ssr" name="citation_author" content="Yunkai Lv"><meta data-n-head="ssr" name="prism.issn" content="ISSN 2770-3541 (Online)"><meta data-n-head="ssr" name="prism.publicationName" content="OAE Publishing Inc."><meta data-n-head="ssr" name="prism.publicationDate" content="2024-09-24"><meta data-n-head="ssr" name="prism.volume" content="4"><meta data-n-head="ssr" name="prism.section" content="Review"><meta data-n-head="ssr" name="prism.startingPag" content="293"><meta data-n-head="ssr" name="prism.url" content="https://www.oaepublish.com/articles/ir.2024.19"><meta data-n-head="ssr" name="prism.doi" content="doi:10.20517/ir.2024.19"><meta data-n-head="ssr" name="citation_journal_abbrev" content="ir"><meta data-n-head="ssr" name="citation_article_type" content="Review"><meta data-n-head="ssr" name="citation_language" content="en"><meta data-n-head="ssr" name="citation_doi" content="10.20517/ir.2024.19"><meta data-n-head="ssr" name="citation_id" content="ir.2024.19"><meta data-n-head="ssr" name="citation_issn" content="ISSN 2770-3541 (Online)"><meta data-n-head="ssr" name="citation_publication_date" content="2024-09-24"><meta data-n-head="ssr" name="citation_author_institution" content="Correspondence to: Prof. Huaicheng Yan, Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China. E-mail: hcyan@ecust.edu.cn"><meta data-n-head="ssr" name="citation_pdf_url" content="https://f.oaes.cc/xmlpdf/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019.pdf"><meta data-n-head="ssr" name="citation_fulltext_html_url" content="https://www.oaepublish.com/articles/ir.2024.19"><meta data-n-head="ssr" name="fulltext_pdf" content="https://f.oaes.cc/xmlpdf/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019.pdf"><meta data-n-head="ssr" name="twitter:type" content="article"><meta data-n-head="ssr" name="twitter:title" content="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review"><meta data-n-head="ssr" name="twitter:description" content="This paper reviews the application of distributed model predictive control (DMPC) for autonomous intelligent systems (AIS) with unmanned aerial vehicles (UAVs) and vehicle platoon systems. DMPC is an optimal control method that formulates and solves optimization problems to adjust control strategies by predicting future states based on system models while managing constraints, and this technique has been applied to an increasing number of industrial areas. As the essential parts of AIS, UAVs and vehicle platoon systems have received extensive attention in the civil, industrial, and military fields. DMPC has the ability to quickly solve optimization problems in real-time while taking into account the prediction of the future state of the system, which fits in well with the ability of AIS to predict the environment when making decisions, so the application of DMPC in AIS has a natural advantage. This paper first introduces the basic principles of DMPC and the theoretical results in multi-agent systems (MASs). It then reviews the application of DMPC methods to UAVs and vehicle platoon systems. Finally, the challenges of the existing methods are summarized to offer insights to advance the future development of DMPC in practical applications."><meta data-n-head="ssr" name="og:url" content="https://www.oaepublish.com/articles/ir.2024.19"><meta data-n-head="ssr" name="og:type" content="article"><meta data-n-head="ssr" name="og:site_name" content="Intelligence & Robotics"><meta data-n-head="ssr" name="og:title" content="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review"><meta data-n-head="ssr" name="og:description" content="This paper reviews the application of distributed model predictive control (DMPC) for autonomous intelligent systems (AIS) with unmanned aerial vehicles (UAVs) and vehicle platoon systems. DMPC is an optimal control method that formulates and solves optimization problems to adjust control strategies by predicting future states based on system models while managing constraints, and this technique has been applied to an increasing number of industrial areas. As the essential parts of AIS, UAVs and vehicle platoon systems have received extensive attention in the civil, industrial, and military fields. DMPC has the ability to quickly solve optimization problems in real-time while taking into account the prediction of the future state of the system, which fits in well with the ability of AIS to predict the environment when making decisions, so the application of DMPC in AIS has a natural advantage. This paper first introduces the basic principles of DMPC and the theoretical results in multi-agent systems (MASs). It then reviews the application of DMPC methods to UAVs and vehicle platoon systems. Finally, the challenges of the existing methods are summarized to offer insights to advance the future development of DMPC in practical applications."><title>Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review</title><link data-n-head="ssr" rel="icon" type="image/x-icon" href="/favicon.ico"><link data-n-head="ssr" rel="canonical" href="https://www.oaepublish.com/articles/ir.2024.19"><script data-n-head="ssr" src="https://accounts.google.com/gsi/client" async></script><script data-n-head="ssr" src="https://g.oaes.cc/oae/dist/relijs.js" async></script><link rel="preload" href="https://g.oaes.cc/oae/nuxt/47b9fdf.js" as="script"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/800bc65.js" as="script"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/css/8176b15.css" as="style"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/d5348f9.js" as="script"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/css/1048d89.css" as="style"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/7bf631b.js" as="script"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/css/9f35d97.css" as="style"><link rel="preload" href="https://g.oaes.cc/oae/nuxt/5b7fe78.js" as="script"><link rel="stylesheet" href="https://g.oaes.cc/oae/nuxt/css/8176b15.css"><link rel="stylesheet" href="https://g.oaes.cc/oae/nuxt/css/1048d89.css"><link rel="stylesheet" href="https://g.oaes.cc/oae/nuxt/css/9f35d97.css"> </head> <body > <div data-server-rendered="true" id="__nuxt"><!----><div id="__layout"><div data-fetch-key="data-v-0bee1158:0" data-v-0bee1158><div class="PcComment" data-v-5c01d453 data-v-0bee1158><div class="ipad_bg" style="display:none;" data-v-5c01d453></div> <div class="head_top" data-v-5c01d453><div class="wrapper head_box" data-v-5c01d453><span class="qk_jx" data-v-5c01d453><img src="https://i.oaes.cc/upload/journal_logo/ir.png" alt data-v-5c01d453></span> <a href="/ir" class="qk_a_name" data-v-5c01d453><span class="title font20" data-v-5c01d453>Intelligence & Robotics</span></a> <i class="el-icon-caret-right sjbtn" style="color:rgb(0,71,187);" data-v-5c01d453></i> <div class="top_img" data-v-5c01d453><a href="https://www.scopus.com/sourceid/21101199351" target="_blank" data-v-5c01d453><img src="https://i.oaes.cc/uploads/20240813/49390c7e86ab40a58ee862e8c1af65ba.png" alt data-v-5c01d453></a><a href="" target="_blank" data-v-5c01d453><img src="https://i.oaes.cc/uploads/20240506/ea3d9071c35b4bf3982ffe25f1083620.png" alt data-v-5c01d453></a></div> <div class="oae_menu_box" data-v-5c01d453><a href="/alljournals" data-v-5c01d453><span data-v-5c01d453>All Journals</span></a></div> <span class="search" data-v-5c01d453><i class="icon-search icon_right font24" data-v-5c01d453></i> <span data-v-5c01d453>Search</span></span> <span class="go_oae" data-v-5c01d453><a href="https://www.oaecenter.com/login" target="_blank" data-v-5c01d453><i class="icon-login-line icon_right font24" data-v-5c01d453></i> <span data-v-5c01d453>Log In</span></a></span></div></div> <div class="cg" style="height: 41px" data-v-5c01d453></div> <!----> <div class="head_text" style="border-bottom:3px solid rgb(0,71,187);" data-v-5c01d453><div class="head_search wrapper" style="display:none;" data-v-5c01d453><div class="box_btn" data-v-5c01d453><div class="qk_miss" data-v-5c01d453><img src="https://i.oaes.cc/uploads/20250113/159ddc46c12d440d82d12f7fc8013e88.jpg" alt class="qk_fm" data-v-5c01d453> <div class="miss_right" data-v-5c01d453><div class="miss_btn" data-v-5c01d453><span data-v-5c01d453><span class="font_b" data-v-5c01d453>Editor-in-Chief:</span> Simon X. 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class="font-999" data-v-49c221b8>23 Sep 2024</span></div> <div class="tit_box mgt30" data-v-49c221b8><h1 id="art_title" class="art_title2" data-v-49c221b8><span data-v-49c221b8>Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review</span><!----></h1> <div class="art_seltte" data-v-49c221b8><div class="el-dropdown" style="width:140px;" data-v-49c221b8><button type="button" class="el-button el-button--primary" style="width:140px;padding:10px 6px;background:#4475e1 !important;border:1px solid #4475e1 !important;" data-v-49c221b8><!----><!----><span><span style="display:flex;align-items:center;justify-content:center;" data-v-49c221b8><img 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class="Crossref" data-v-49c221b8> <span data-v-49c221b8>0</span> <!----></span></div> <div id=" authorString" class="article-authors" data-v-49c221b8><span class="authors_item" data-v-49c221b8><div affNumList="" data-v-dc220f24 data-v-49c221b8><span class="pos_re" data-v-dc220f24><div role="tooltip" id="el-popover-8628" aria-hidden="true" class="el-popover el-popper" style="width:300px;display:none;"><!----><h3 class="font16 no_sup" style="color:#333;margin-bottom:20px;" data-v-dc220f24>Yang Peng<sup></sup></h3> <div class="Aff_current font14 no_sup" data-v-dc220f24><div data-v-dc220f24><div class="author_cont" data-v-dc220f24><label></label><addr-line>Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China. </addr-line></div></div></div> <i class="close_btn el-icon-close" data-v-dc220f24></i> <a href="https://scholar.google.com/scholar?q=Yang Peng" target="_blank" data-v-dc220f24><button type="button" class="el-button el-button--primary el-button--mini" data-v-dc220f24><!----><!----><span>Google Scholar</span></button></a></div><span class="el-popover__reference-wrapper"><span class="author_name" data-v-dc220f24>Yang Peng<sup></sup></span></span></span></div> <a href="https://orcid.org/0009-0008-0113-850X" target="_blank" data-v-49c221b8><img alt="" src="https://g.oaes.cc/oae/nuxt/img/orcid.a3b6f80.png" class="id_img" data-v-49c221b8></a> <!----> <!----> <!----> <i data-v-49c221b8> , </i></span><span class="authors_item" data-v-49c221b8><div affNumList="" data-v-dc220f24 data-v-49c221b8><span class="pos_re" data-v-dc220f24><div role="tooltip" id="el-popover-9572" aria-hidden="true" class="el-popover el-popper" style="width:300px;display:none;"><!----><h3 class="font16 no_sup" style="color:#333;margin-bottom:20px;" data-v-dc220f24>Huaicheng Yan<sup></sup></h3> <div class="Aff_current font14 no_sup" data-v-dc220f24><div data-v-dc220f24><div class="author_cont" data-v-dc220f24><label></label><addr-line>Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China. </addr-line></div></div></div> <i class="close_btn el-icon-close" data-v-dc220f24></i> <a href="https://scholar.google.com/scholar?q=Huaicheng Yan" target="_blank" data-v-dc220f24><button type="button" class="el-button el-button--primary el-button--mini" data-v-dc220f24><!----><!----><span>Google Scholar</span></button></a></div><span class="el-popover__reference-wrapper"><span class="author_name" data-v-dc220f24>Huaicheng Yan<sup></sup></span></span></span></div> <a href="https://orcid.org/0000-0001-5496-1809" target="_blank" data-v-49c221b8><img alt="" src="https://g.oaes.cc/oae/nuxt/img/orcid.a3b6f80.png" class="id_img" data-v-49c221b8></a> <!----> <!----> <!----> <i data-v-49c221b8> , ... </i></span><span class="authors_item" data-v-49c221b8><!----></span><span class="authors_item" data-v-49c221b8><!----></span><span class="authors_item" data-v-49c221b8><div affNumList="" data-v-dc220f24 data-v-49c221b8><span class="pos_re" data-v-dc220f24><div role="tooltip" id="el-popover-8456" aria-hidden="true" class="el-popover el-popper" style="width:300px;display:none;"><!----><h3 class="font16 no_sup" style="color:#333;margin-bottom:20px;" data-v-dc220f24>Yunkai Lv<sup></sup></h3> <div class="Aff_current font14 no_sup" data-v-dc220f24><div data-v-dc220f24><div class="author_cont" data-v-dc220f24><label></label><addr-line>Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China. </addr-line></div></div></div> <i class="close_btn el-icon-close" data-v-dc220f24></i> <a href="https://scholar.google.com/scholar?q=Yunkai Lv" target="_blank" data-v-dc220f24><button type="button" class="el-button el-button--primary el-button--mini" data-v-dc220f24><!----><!----><span>Google Scholar</span></button></a></div><span class="el-popover__reference-wrapper"><span class="author_name" data-v-dc220f24>Yunkai Lv<sup></sup></span></span></span></div> <a href="https://orcid.org/0000-0001-5212-8629" target="_blank" data-v-49c221b8><img alt="" src="https://g.oaes.cc/oae/nuxt/img/orcid.a3b6f80.png" class="id_img" data-v-49c221b8></a> <!----> <!----> <!----> <!----></span> <button type="button" class="el-button el-button--primary el-button--mini" data-v-49c221b8><!----><i class="el-icon-plus"></i><span>Show Authors</span></button></div> <div class="article-header-info" data-v-49c221b8><div data-v-49c221b8> <i>Intell Robot</i> 2024;4(3):293-317.</div> <div class="mgt5" data-v-49c221b8><a href="https://doi.org/10.20517/ir.2024.19" target="_blank" data-v-49c221b8>10.20517/ir.2024.19</a> | <span class="btn_link" data-v-49c221b8>© The Author(s) 2024.</span></div></div> <div class="top_btn_box" data-v-49c221b8><div class="btn_item" data-v-49c221b8><i class="el-icon-caret-right" data-v-49c221b8></i><span data-v-49c221b8>Author Information</span></div> <div class="btn_item" data-v-49c221b8><i class="el-icon-caret-right" data-v-49c221b8></i><span data-v-49c221b8>Article Notes</span></div> <div class="btn_item" data-v-49c221b8><i class="el-icon-caret-right" data-v-49c221b8></i><span data-v-49c221b8>Cite This Article</span></div></div> <div class="author_box" style="display:none;" data-v-49c221b8><div data-v-49c221b8><div data-v-49c221b8><label></label><addr-line>Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China. </addr-line></div></div> <div class="CorrsPlus" data-v-49c221b8><div data-v-49c221b8><span id="cirrsMail" data-v-49c221b8>Correspondence to: Prof. Huaicheng Yan, Key Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China. E-mail: <email>hcyan@ecust.edu.cn</email></span></div></div></div> <div class="notes_box" style="display:none;" data-v-49c221b8><div class="articleDate mag_top10" data-v-49c221b8><span><b>Received:</b> 3 Apr 2024 | </span><span><b>First Decision:</b> 1 Aug 2024 | </span><span><b>Revised:</b> 5 Sep 2024 | </span><span><b>Accepted:</b> 11 Sep 2024 | </span><span><b>Published:</b> 24 Sep 2024</span></div> <div class="articleDate" data-v-49c221b8><span><b>Academic Editor:</b> Simon X. Yang | </span><span><b>Copy Editor:</b> Pei-Yun Wang | </span><span><b>Production Editor:</b> Pei-Yun Wang</span></div></div> <div class="article_bg" data-v-49c221b8><h2 id="art_Abstract" data-v-49c221b8>Abstract<!----></h2> <div id="seo_des" class="article_Abstract mag_btn10" data-v-49c221b8><p>This paper reviews the application of distributed model predictive control (DMPC) for autonomous intelligent systems (AIS) with unmanned aerial vehicles (UAVs) and vehicle platoon systems. DMPC is an optimal control method that formulates and solves optimization problems to adjust control strategies by predicting future states based on system models while managing constraints, and this technique has been applied to an increasing number of industrial areas. As the essential parts of AIS, UAVs and vehicle platoon systems have received extensive attention in the civil, industrial, and military fields. DMPC has the ability to quickly solve optimization problems in real-time while taking into account the prediction of the future state of the system, which fits in well with the ability of AIS to predict the environment when making decisions, so the application of DMPC in AIS has a natural advantage. This paper first introduces the basic principles of DMPC and the theoretical results in multi-agent systems (MASs). It then reviews the application of DMPC methods to UAVs and vehicle platoon systems. Finally, the challenges of the existing methods are summarized to offer insights to advance the future development of DMPC in practical applications.</p></div> <div class="img_jj" data-v-49c221b8><h2 id="art_Graphical" data-v-49c221b8>Graphical Abstract</h2> <div class="article_Abstract" data-v-49c221b8></div> <img src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-coverimg.big.jpg" alt="" data-v-49c221b8> <div class="img_btn" data-v-49c221b8><a href="/articles//abstimg/" target="_blank" data-v-49c221b8><button type="button" class="el-button el-button--primary" data-v-49c221b8><!----><!----><span>Open in new tab</span></button></a> <a href="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-coverimg.jpg" target="_blank" data-v-49c221b8><button type="button" class="el-button el-button--primary" data-v-49c221b8><!----><!----><span>Download high-res image</span></button></a></div></div> <h2 id="art_Keywords" data-v-49c221b8>Keywords<!----></h2> <div class="article_Abstract" data-v-49c221b8><span id="seo_key" data-v-49c221b8>Distributed model predictive control, autonomous intelligent systems, multi-agent systems, unmanned aerial vehicles, vehicle platoon systems</span></div></div> <div class="MoComment" data-v-49c221b8><div class="top_banner" data-v-49c221b8><!----> <div class="line" data-v-49c221b8></div> <div class="img_box" data-v-49c221b8><!----> <!----></div></div> <!----> <div class="article_link" data-v-49c221b8><span data-v-49c221b8><a href="https://f.oaes.cc/xmlpdf/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019_down.pdf?v=22" data-v-49c221b8><b data-v-49c221b8><i class="icon-download icon_right4" data-v-49c221b8></i> Download PDF</b></a></span> <span data-v-49c221b8><i class="comment-l icon-commentl iconfont icon_right4" data-v-49c221b8></i> <!----><b data-v-49c221b8>0</b></span> <span data-v-49c221b8><span data-v-49c221b8><div role="tooltip" id="el-popover-549" aria-hidden="true" class="el-popover el-popper" style="width:170px;display:none;"><!----><div class="icon_share" style="text-align:right;margin:0;" data-v-49c221b8><a href="http://pinterest.com/pin/create/button/?url=&media=&description=https://www.oaepublish.com/articles/" target="_blank" class="pinterest-sign" data-v-49c221b8><i class="iconfont icon-pinterest" data-v-49c221b8></i></a> <a href="https://www.facebook.com/sharer/sharer.php?u=https://www.oaepublish.com/articles/" target="_blank" class="facebook-sign" data-v-49c221b8><i aria-hidden="true" class="iconfont icon-facebook" data-v-49c221b8></i></a> <a href="https://twitter.com/intent/tweet?url=https://www.oaepublish.com/articles/" target="_blank" class="twitter-sign" data-v-49c221b8><i class="iconfont icon-tuite1" data-v-49c221b8></i></a> <a href="https://www.linkedin.com/shareArticle?url=https://www.oaepublish.com/articles/" target="_blank" class="linkedin-sign" data-v-49c221b8><i class="iconfont icon-linkedin" data-v-49c221b8></i></a></div> </div><span class="el-popover__reference-wrapper"><button type="button" class="el-button colorddd el-button--text el-button--mini" data-v-49c221b8><!----><!----><span><i class="icon-fenxiang iconfont icon_right4" data-v-49c221b8></i> <!----><b data-v-49c221b8>2</b></span></button></span></span></span> <span data-v-49c221b8><span class="no_zan" data-v-49c221b8><i class="icon-like-line icon_right4" data-v-49c221b8></i> <!----><i class="num_n" data-v-49c221b8><b data-v-49c221b8>15</b></i></span></span></div></div> <div id="artDivBox" class="art_cont" data-v-49c221b8><div id="s1" class="article-Section"><h2 >1. INTRODUCTION</h2><p class="">With the rapid development of communication technology and computer science, the deep integration of complex systems and sensing decision-making has gained unprecedented development<sup>[<a href="#b1" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b1">1</a>,<a href="#b2" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b2">2</a>]</sup>. Autonomous intelligent systems (AIS) are capable of environmental sensing, target detection, and cooperative control through the integration of advanced control, communication modules, and sensing technologies. They have the ability to autonomously plan actions, share resources, and operate remotely to complete tasks<sup>[<a href="#b3" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b3">3</a>]</sup>. AIS is increasingly being used in civil and industrial fields, such as logistics and transportation<sup>[<a href="#b4" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b4">4</a>]</sup>, power system inspection, and ocean exploration, as well as military fields<sup>[<a href="#b5" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b5">5</a>]</sup>, including demining and blasting, battlefield surveillance, and combat confrontation. Their unique capability to replace humans in complex and high-risk environments renders them invaluable tools. However, as task demands grow in difficulty and complexity, single unmanned systems face limitations in information access and problem-solving capacity. It is necessary for AIS to deal with current difficulties through a distributed approach, which offers advantages such as spatial distribution, parallel task execution, and fault tolerance. AIS has become a new trend in future research due to its comprehensive information acquisition and ability to realize intelligent interaction and processing in response to mission requirements, compared to single-unmanned systems.</p><p class="">The AIS must perceive the environment to perform autonomous planning, and the prediction part of planning can be realized by optimizing the future state through the distributed model predictive control (DMPC) method. As an optimal control algorithm based on an optimization problem that can handle constraints efficiently, DMPC is widely used in power systems<sup>[<a href="#b6" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b6">6</a>]</sup>, chemical processes<sup>[<a href="#b7" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b7">7</a>]</sup>, urban transportation<sup>[<a href="#b8" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b8">8</a>]</sup>, and manufacturing systems<sup>[<a href="#b9" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b9">9</a>]</sup>. As a distributed online rolling computation algorithm, DMPC allows AIS to navigate physical and environmental constraints, making it increasingly popular in AIS applications.</p><p class="">As the crucial components of AIS, the cooperative control of unmanned aerial vehicles (UAVs) and vehicle platoon systems has received much attention. UAVs play a vital role in several fields, such as disaster relief, environmental monitoring, logistics, transportation, and military surveillance. Through cooperative control, UAVs can quickly and efficiently cover large areas, perform complex missions, and enhance the response speed and success rates of missions<sup>[<a href="#b10" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b10">10</a>-<a href="#b12" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b12">12</a>]</sup>, and vehicle platooning systems achieve efficient fleet management, reduce traffic congestion, and save energy consumption in various scenarios such as freight transportation, autonomous driving, and traffic management in modern urban environments, thus improving transportation efficiency and road safety<sup>[<a href="#b13" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b13">13</a>-<a href="#b15" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b15">15</a>]</sup>. The difference between UAVs and vehicle platoon systems is that UAVs operate in a three-dimensional airspace, relying on technologies such as GPS, inertial navigation systems, and radar. In contrast, vehicle platoons operate in a two-dimensional road network, responding to traffic regulations, road conditions, and other vehicles, often using vehicle-to-everything (V2X) communications and light detection and ranging (LiDAR) technologies. UAVs have a more limited range due to battery limitations, while vehicle platoons are more accessible to refuel or recharge and have a longer range. However, UAVs and vehicle platoon systems are similar in several ways, e.g., both involve cooperative control of multiple independent units and require real-time decision-making and communication to achieve common goals; both require real-time control in a dynamic and uncertain environment to ensure efficient operation and safety; both need to consider physical and network security. Despite some differences, UAVs and vehicle platoon systems share commonalities in core technologies such as cooperative control, multi-subsystems communication and path optimization, all of which can be effectively handled under the framework of DMPC. Meanwhile, considering the significance of the cooperative operation between UAVs and vehicle platoon systems in both civil and military fields, an overview of the two systems can help to promote the integration of the two fields, inspire researchers to explore the cooperative operation of these two systems and promote the development of integrated solutions in AIS.</p><p class="">Although existing review articles have covered a wide range of research on DMPC in different application scenarios, such as smart grids<sup>[<a href="#b16" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b16">16</a>-<a href="#b18" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b18">18</a>]</sup>, networked control systems<sup>[<a href="#b19" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b19">19</a>]</sup>, autonomous ground vehicles (AGVs)<sup>[<a href="#b20" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b20">20</a>]</sup>, each has specific focuses and limitations. For example, Arauz <i>et al</i>. concentrated on the application of DMPC in network control problems, with special emphasis on its vulnerabilities and defense mechanisms in network security<sup>[<a href="#b19" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b19">19</a>]</sup>. On the other hand, Yu <i>et al</i>. comprehensively reviewed the application of model predictive control (MPC) in single and multiple AGVs<sup>[<a href="#b20" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b20">20</a>]</sup>. Notably, Negenborn <i>et al</i>. surveyed and categorized a wide range of DMPC methods, offering insights into the historical development and research trends of these methods<sup>[<a href="#b21" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b21">21</a>]</sup>. However, none of these reviews have specifically addressed the application of DMPC to two critical domains - UAVs and vehicle platoon systems nor have they discussed the unique challenges and future research directions for DMPC within these systems.</p><p class="">In contrast to existing reviews, this review systematically introduces the basic fundamentals of DMPC and its theoretical achievements in multi-agent systems (MASs), with a unique focus on the application of DMPC in two AIS subsystems: UAVs and vehicle platoon systems. It also highlights the shortcomings and challenges of the existing methods in practical applications and discusses the direction of future research to promote DMPC in UAVs and vehicle platoon systems. This review presents the basics of DMPC with theoretical foundations in MASs in Section 2. Sections 3 and 4 review the DMPC applications in UAVs and vehicle platoon systems, respectively. Section 5 discusses the existing shortcomings and challenges of the DMPC approach for AIS. Finally, the conclusion is provided in Section 6.</p></div><div id="s2" class="article-Section"><h2 >2. PRELIMINARY FOR DMPC</h2><p class="">Before introducing the application of DMPC in UAVs and vehicle platoon systems, this section will introduce the basics of DMPC and the advances of its theoretical research in MASs.</p><div id="s2-1" class="article-Section"><h3 >2.1 MPC</h3><p class="">MPC is derived from optimal control, which computes for a sequence of control inputs by optimizing a cost function containing information about the system's states and control inputs at a future time and explicitly handling the constraints imposed on the system<sup>[<a href="#b22" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b22">22</a>]</sup>. MPC employs a rolling optimization strategy, which optimizes over a finite time horizon. Considering a discrete-time system <inline-formula><tex-math id="M1">$$ x(t+1)=f(x(t), u(t)) $$</tex-math></inline-formula> as an example, where the system is sampled at a specific sampling instant <inline-formula><tex-math id="M2">$$ t $$</tex-math></inline-formula>, and the currently sampled state information <inline-formula><tex-math id="M3">$$ x(t) $$</tex-math></inline-formula> is used as the initial state based on the model of the system to predict the state of the system in the prediction horizon <inline-formula><tex-math id="M4">$$ [t, t+N] $$</tex-math></inline-formula>. Simultaneously, a constrained open-loop optimization problem is solved for a given system cost function to obtain a set of control input sequences. The first control input in this sequence is then applied to the actual controlled system. The new state of the system is obtained by sampling at the next sampling instant <inline-formula><tex-math id="M5">$$ t+1 $$</tex-math></inline-formula>, and this process is performed repeatedly. The specific process is shown in <a href="#Figure1" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure1">Figure 1</a>.</p><div class="Figure-block" id="Figure1"><div xmlns="http://www.w3.org/1999/xhtml" class="article-figure-image"><a href="/articles/ir.2024.19/image/Figure1" class="Article-img" alt="" target="_blank"><img alt="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review" src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-1.jpg" class="" title="" alt="" /></a></div><div class="article-figure-note"><p class="figure-note"></p><p class="figure-note">Figure 1. MPC strategy. MPC: Model predictive control.</p></div></div><p class="">MPC has been widely used in linear systems<sup>[<a href="#b23" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b23">23</a>,<a href="#b24" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b24">24</a>]</sup> and nonlinear systems<sup>[<a href="#b25" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b25">25</a>,<a href="#b26" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b26">26</a>]</sup>, but it is not the focus of this paper. There are quite a few foundations for MPC research, such as robust MPC methods to cope with external disturbances<sup>[<a href="#b27" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b27">27</a>-<a href="#b29" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b29">29</a>]</sup>, tracking MPC methods to achieve the designed control objectives<sup>[<a href="#b30" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b30">30</a>,<a href="#b31" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b31">31</a>]</sup>, and economic model predictive control (EMPC) methods considering economic costs in the actual production process<sup>[<a href="#b32" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b32">32</a>]</sup>. Recently, the data-driven MPC methods were proposed by Berberich <i>et al</i>., and a rigorous theoretical analysis was given<sup>[<a href="#b31" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b31">31</a>,<a href="#b33" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b33">33</a>,<a href="#b34" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b34">34</a>]</sup>. For more information about the advances in theoretical research on MPC and the application of MPC methods in robotics, UAVs, and other systems, readers can refer to Ref.<sup>[<a href="#b35" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b35">35</a>-<a href="#b39" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b39">39</a>]</sup>.</p></div><div id="s2-2" class="article-Section"><h3 >2.2 DMPC</h3><p class="">As the scale of engineering systems increases, the applicability of traditional MPC methods diminishes. Instead, the DMPC method has received more attention for its excellent capability of dealing with complex large-scale systems characterized by high dimensionality, multiple subsystems, constraints, and targets. Unlike the centralized architecture of traditional MPC methods, DMPC decomposes the global system into several subsystems and formulates a local optimization problem for each subsystem, allowing the complex optimization problem of a large-scale system to be divided into simple subproblems. This approach significantly reduces the scale and computational complexity of individual optimization problems<sup>[<a href="#b40" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b40">40</a>]</sup>. A quantitative comparison of some key performances between centralized MPC and DMPC is shown in <a href="#Figure2" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure2">Figure 2</a>. With the DMPC strategy, information can be exchanged between subsystems, and interaction is also allowed between the local model prediction controllers of each subsystem. The structure of DMPC is schematically illustrated in <a href="#Figure3" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure3">Figure 3</a>.</p><div class="Figure-block" id="Figure2"><div xmlns="http://www.w3.org/1999/xhtml" class="article-figure-image"><a href="/articles/ir.2024.19/image/Figure2" class="Article-img" alt="" target="_blank"><img alt="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review" src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-2.jpg" class="" title="" alt="" /></a></div><div class="article-figure-note"><p class="figure-note"></p><p class="figure-note">Figure 2. Quantitative comparison of key performances between centralized MPC and DMPC. MPC: Model predictive control; DMPC: distributed model predictive control.</p></div></div><div class="Figure-block" id="Figure3"><div xmlns="http://www.w3.org/1999/xhtml" class="article-figure-image"><a href="/articles/ir.2024.19/image/Figure3" class="Article-img" alt="" target="_blank"><img alt="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review" src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-3.jpg" class="" title="" alt="" /></a></div><div class="article-figure-note"><p class="figure-note"></p><p class="figure-note">Figure 3. DMPC structure. DMPC: Distributed model predictive control.</p></div></div><p class="">In the following, a commonly used DMPC standard framework will be introduced, including the determination of optimization problem, cost function, and information transmission in DMPC.</p><div id="s2-2-1" class="article-Section"><h4 >2.2.1 Optimization problem</h4><p class="">A general discrete system is taken as an example to introduce the optimization problem of DMPC:</p><p class=""><div class="disp-formula"><label>(1)</label><tex-math id="E1"> $$ \begin{equation} x_i(t+1)=f_i(x_i(t), u_i(t), x_{-i}(t)) \end{equation} $$ </tex-math></div></p><p class="">where <inline-formula><tex-math id="M6">$$ x_i(t) \in \mathbb{R}^{n_i} $$</tex-math></inline-formula>, <inline-formula><tex-math id="M7">$$ u_i(t) \in \mathbb{R}^{m_i} $$</tex-math></inline-formula> denote the state and control input vector of the subsystem <inline-formula><tex-math id="M8">$$ i $$</tex-math></inline-formula>, respectively, and <inline-formula><tex-math id="M9">$$ x_{-i}(t) $$</tex-math></inline-formula> represents the state of the subsystem that has information interaction with subsystem <inline-formula><tex-math id="M10">$$ i $$</tex-math></inline-formula>. Furthermore, the system states and the control inputs must satisfy the constraints: <inline-formula><tex-math id="M11">$$ x_i(t)\in \mathbb{X}_i $$</tex-math></inline-formula> and <inline-formula><tex-math id="M12">$$ u_i(t)\in \mathbb{U}_i $$</tex-math></inline-formula>, respectively, where <inline-formula><tex-math id="M13">$$ \mathbb{X}_i $$</tex-math></inline-formula> and <inline-formula><tex-math id="M14">$$ \mathbb{U}_i $$</tex-math></inline-formula> are convex sets containing the origin.</p><p class="">In DMPC, each subsystem optimizes only its local cost function, and its local optimization problem is given as:</p><p class=""><div class="disp-formula"><label>（2）</label><tex-math id="E2"> $$ \min\limits_{u_i(t+s|t)}J_i(x_i, u_i, x_{-i}) $$ </tex-math></div></p><p class=""><div class="disp-formula"><label>(2a)</label><tex-math id="E2a"> $$ \begin{align*} s.t.\;\;&x_i(t+s+1|t)=f_i(x_i(t+s|t), u_i(t+s|t), x_{-i}(t+s|t)) \end{align*} $$ </tex-math></div></p><p class=""><div class="disp-formula"><label>(2b)</label><tex-math id="E2b"> $$ \begin{align*} &{x}_i(t|t)=x_i(t) \end{align*} $$ </tex-math></div></p><p class=""><div class="disp-formula"><label>(2c)</label><tex-math id="E2c"> $$ \begin{align*} &x_i(t+s|t) \in \mathbb{X}_i \end{align*} $$ </tex-math></div></p><p class=""><div class="disp-formula"><label>(2d)</label><tex-math id="E2d"> $$ \begin{align*} &u_i(t+s|t) \in \mathbb{U}_i \end{align*} $$ </tex-math></div></p><p class=""><div class="disp-formula"><label>(2e)</label><tex-math id="E2e"> $$ \begin{align*} &x_i(t+N|t) \in \mathbb{X}_f^i \end{align*} $$ </tex-math></div></p><p class="">where <inline-formula><tex-math id="M15">$$ s = 1, ..., N-1 $$</tex-math></inline-formula>, <inline-formula><tex-math id="M16">$$ J_i(x_i, u_i, x_{-i}) $$</tex-math></inline-formula> is the objective cost function of the problem, and <inline-formula><tex-math id="M17">$$ x_i(t+s|t) $$</tex-math></inline-formula> is the state predicted at instant <inline-formula><tex-math id="M18">$$ t $$</tex-math></inline-formula> for the instant <inline-formula><tex-math id="M19">$$ t+s $$</tex-math></inline-formula>. The terminal term <inline-formula><tex-math id="M20">$$ x_i(t+N|t) \in \mathbb{X}_f^i $$</tex-math></inline-formula> is often used to ensure the stability of the system.</p></div><div id="s2-2-2" class="article-Section"><h4 >2.2.2 Cost function</h4><p class="">The cost function <inline-formula><tex-math id="M21">$$ J_i $$</tex-math></inline-formula> defines the control objectives of the system and guides the direction of the optimization process. However, since different tasks have varying requirements, the design of the cost function must be adapted to specific application scenarios. For instance, in UAV formation control, the cost function may prioritize maintaining formation shape and avoiding collisions, whereas in vehicle platooning, it might emphasize speed coordination and fuel efficiency. Therefore, the formulation of the cost function should not only be consistent with the overall objectives of the control system but should also accurately reflect the specific demands of a given task, thereby enabling efficient and cooperative control in a complex system. The following is a common form of DMPC cost function:</p><p class=""><div class="disp-formula"><label>(3)</label><tex-math id="E3"> $$ \begin{equation} J_i= \sum\limits_{s=0}^{N-1} l(x_i(t+s|t), u_i(t+s|t))+V_c(x_i(t+s|t), x_{-i}(t+s|t))+V_f(x_i(t+N|t)) \end{equation} $$ </tex-math></div></p><p class="">Here, <inline-formula><tex-math id="M22">$$ l(x_i(t+s|t), u_i(t+s|t) $$</tex-math></inline-formula> represents the stage cost at the instant <inline-formula><tex-math id="M23">$$ t+s $$</tex-math></inline-formula>, and <inline-formula><tex-math id="M24">$$ V_c(x_i(t+s|t), x_{-i}(t+s|t)) $$</tex-math></inline-formula> denotes the coupling cost term that containing the state of both subsystem <inline-formula><tex-math id="M25">$$ i $$</tex-math></inline-formula> and its neighbors. Additionally, in DMPC, it is often necessary to include a coupling cost that incorporates information about neighboring subsystems in the cost function. The information transmission between the neighbors will be introduced in the following sections.</p></div><div id="s2-2-3" class="article-Section"><h4 >2.2.3 Information transmission</h4><p class="">In DMPC, the interaction of information between subsystems and the sequence of solving the optimization problem is critical for achieving efficient cooperative control. Typically, the sequence of optimization problem solving and transmission can be categorized into three approaches: The first is sequential solving and transmission, where each subsystem sequentially solves the problem in a predetermined order and transmits the results to other related subsystems. The advantage of this approach lies in its clear flow and easy-to-implement sequence control, but it may lead to delays in the overall system. The second approach is synchronous solving and transmission, where all the subsystems start solving simultaneously and transmit the information at the same instant, which minimizes the latency but requires high communication and computational resources. The third approach is asynchronous solving and transmission, where each subsystem independently completes the solving and transmission on its own time scale, allowing for a certain degree of non-simultaneity and thus increasing system flexibility. To illustrate the different characteristics of these approaches more intuitively, <a href="#Figure4" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure4">Figure 4</a> presents the sequences of optimization problem-solving and information transmission in the DMPC strategy for a MAS with three agents as an example.</p><div class="Figure-block" id="Figure4"><div xmlns="http://www.w3.org/1999/xhtml" class="article-figure-image"><a href="/articles/ir.2024.19/image/Figure4" class="Article-img" alt="" target="_blank"><img alt="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review" src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-4.jpg" class="" title="" alt="" /></a></div><div class="article-figure-note"><p class="figure-note"></p><p class="figure-note">Figure 4. Information interaction between subsystems and the sequence of solving optimization problems. (A) sequential solving and transmission; (B) synchronous solving and transmission; (C) asynchronous solving and transmission.</p></div></div><p class="">In DMPC, subsystems usually need predictive state information of their neighbors at the current moment in the length of the prediction horizon <inline-formula><tex-math id="M26">$$ N $$</tex-math></inline-formula> to construct the optimization problem. There are generally two main approaches to constructing this predicted state information. The first method is that the neighbor first constructs a complete sequence of predicted states that satisfies the required length of the current subsystem, and then transmits this information to the needed subsystem. The advantage of this approach is that the subsystem can directly utilize the complete information for computation, although it may impose a significant data transmission burden. The second approach is that the neighbor transmits only a part of the necessary state information while the receiver subsystem performs specific calculations based on the received data to construct the necessary neighboring state sequence. This approach can reduce the burden of data transmission, but may require additional computational resources and more complex algorithm design to ensure that the constructed state information can satisfy the requirements of control accuracy. These two methods of information construction enable DMPC to achieve efficient and accurate information interaction and cooperative control in complex systems.</p><p class="">Moreover, existing DMPC algorithms can be classified based on the topology of the transmission network, the information exchange protocols used among local controllers, and the type of cost function considered in the local optimization problem. Depending on whether or not the performance metrics of other subsystems are included in the local cost function, DMPC algorithms can be categorized into coordinated and uncoordinated approaches. Specifically, if each local controller holds global information and minimizes the global cost function, it is referred to as coordinated DMPC<sup>[<a href="#b41" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b41">41</a>-<a href="#b43" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b43">43</a>]</sup>. Conversely, if each local predictive controller possesses local information, considers the information of its neighbors in the network topology, and uses the information of its neighbors as useful information for its local optimization problem and minimizes the local cost function, it is referred to as uncoordinated DMPC<sup>[<a href="#b44" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b44">44</a>-<a href="#b48" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b48">48</a>]</sup>. Compared with coordinated DMPC, in uncoordinated DMPC, each local controller only needs to exchange information with its associated subsystems, which have lower network requirements. Since uncoordinated DMPC only improves its performance during the optimization process, the overall performance of the system is weaker than that of the coordination algorithm based on the global cost function, but it has more flexibility for the control of each subsystem. In most uncoordinated DMPC, local controllers generally use parallel computation to solve the optimization problems of each subsystem simultaneously<sup>[<a href="#b46" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b46">46</a>]</sup>. When controllers operate asynchronously, a corresponding communication strategy for asynchronous transmission is necessary<sup>[<a href="#b47" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b47">47</a>,<a href="#b48" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b48">48</a>]</sup>. In the UAVs and vehicle platoon systems targeted in this paper, most of the studies are based on uncoordinated DMPC.</p></div><div id="s2-2-4" class="article-Section"><h4 >2.2.4 Computational complexity</h4><p class="">To analyze the computational complexity of DMPC, it is first necessary to distinguish between linear and nonlinear systems. In linear systems, the computational complexity of DMPC is relatively low due to the availability of efficient solution methods, such as linear programming (LP) or quadratic programming (QP), which have polynomial-time computational complexity. In contrast, DMPC problems for nonlinear systems necessitate the utilization of nonlinear programming (NLP) methodologies, which are inherently more intricate since the solution process entails a greater number of iterative procedures and possesses a higher computational complexity. Furthermore, as the system state dimension increases and the prediction horizon lengthens, the computational complexity rises. An increase in state dimension results in a larger state space, necessitating greater computational resources for state prediction and optimization at each time step. Additionally, a longer prediction horizon expands the size of the optimization problem, as computations must be performed over a more extended prediction horizon, significantly increasing the computational burden. However, a longer prediction horizon also offers enhanced control performance. Therefore, it is necessary to balance control accuracy and computational complexity to ensure that the system can be optimized and controlled in real-time within a reasonable timeframe.</p></div><div id="s2-2-5" class="article-Section"><h4 >2.2.5 Scalability</h4><p class="">The scalability of coordinated and uncoordinated DMPC schemes, as discussed in the previous section, will be analyzed in the following. For coordinated DMPC, each local controller needs to optimize the local cost function and consider the global information. This implies that as the number of subsystems increases, the computational burden of the controller will increase with the global information. In contrast, most uncoordinated DMPC schemes exhibit better scalability. In uncoordinated DMPC, each local controller only optimizes its local cost function, so the increase in the number of subsystems does not directly affect the computational complexity of each controller. However, although the computational burden does not increase, the rise in the number of subsystems may result in each subsystem interacting with more neighboring systems, increasing the frequency of information exchange and the amount of communication. As the system grows in size, more complex communication networks may introduce additional burdens, such as delayed information delivery and data loss. Therefore, in the application of large-scale systems, despite the superior performance of uncoordinated DMPC in terms of computational complexity, it is still necessary to address the challenges posed by increasingly complex communication topologies to ensure the overall performance and reliability of the system.</p><p class="">Since DMPC methods vary considerably when applied to different physical systems and task requirements, this paper will first briefly review the theoretical results of DMPC to MASs in the following subsection. These results can be utilized in the control of UAVs and vehicle platoon systems, as discussed in this paper.</p></div></div><div id="s2-3" class="article-Section"><h3 >2.3 DMPC in MASs</h3><p class="">This section provides a brief review of the theoretical research on DMPC in MASs, dividing the research problems into three key aspects: the existence of disturbances, limited communication and computing resources, and network unreliability.</p><div id="s2-3-1" class="article-Section"><h4 >2.3.1 The existence of disturbances</h4><p class="">In MASs, different agents collaborate through communication to achieve the given task objectives. As the system becomes larger and more complex, deviations from the actual system during modeling and identification become inevitable. Simultaneously, the complex system is increasingly influenced by the external environment, and these disturbances can be classified as external disturbances. A key research direction in this context is the development of robust DMPC strategies to counter external disturbances. The min-max MPC method, which generates optimal control sequences for the system under the "worst-case" disturbance scenario to ensure robust stability, was first proposed by Campo <i>et al</i>.<sup>[<a href="#b49" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b49">49</a>]</sup>. Jia <i>et al</i>. later extended this method to closed-loop DMPC systems by taking feedback control information into account<sup>[<a href="#b50" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b50">50</a>]</sup>. Wei <i>et al</i>. proposed the min-max DMPC method with a self-triggered scheme for the case of multiple parameter uncertainties and external disturbances to achieve robust control under communication delays<sup>[<a href="#b47" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b47">47</a>]</sup>.</p><p class="">In addition, the robust MPC based on "tube" proposed by Mayne is also a classical approach to deal with disturbance<sup>[<a href="#b51" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b51">51</a>]</sup>. In MASs, for instance, Li <i>et al</i>. utilized the tube method to satisfy local robust constraints and applied a modified alternating direction method of multipliers (ADMM) to solve the optimization problem<sup>[<a href="#b52" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b52">52</a>]</sup>. For disturbed leader-follower systems, Li <i>et al</i>. proposed a fully inclusive control algorithm based on tube-DMPC to deal with the problem that the follower may break away from the convex packet under disturbance<sup>[<a href="#b53" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b53">53</a>]</sup>. Based on the DMPC method and the tube-based auxiliary controller, Li <i>et al</i>. realized the robust control of the MASs<sup>[<a href="#b54" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b54">54</a>]</sup>.</p></div><div id="s2-3-2" class="article-Section"><h4 >2.3.2 Limited communication and computing resources</h4><p class="">In the communication process of MASs, communication resources are usually limited due to network bandwidth constraints. Additionally, the computational ability of subsystems in distributed architectures is generally weak, and their computational resources are valuable. While event-triggered control is a better choice in terms of reducing the number of communications and optimization problem solving, for perturbed systems, achieving better control while saving computational resources is a direction of great interest. Zou <i>et al</i>. proposed an event-triggered scheme using the information of neighbors to achieve a balance between resource usage and control performance for MASs subject to bounded disturbance<sup>[<a href="#b48" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b48">48</a>]</sup>. Yang <i>et al</i>. also proposed a similar adaptive event-triggered DMPC scheme<sup>[<a href="#b55" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b55">55</a>]</sup>. In addition, self-triggered DMPC schemes have gradually received attention due to the reduction of the number of samples in the system. Zhan <i>et al</i>. studied the application of a self-triggered scheme in linear MAS consensus<sup>[<a href="#b56" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b56">56</a>]</sup>, and Mi <i>et al</i>. solved the dynamically decoupled MAS collaboration problem<sup>[<a href="#b57" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b57">57</a>]</sup>. Both Wei <i>et al</i>. and Wang <i>et al</i>. applied the self-triggered scheme to nonlinear MASs<sup>[<a href="#b47" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b47">47</a>,<a href="#b58" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b58">58</a>]</sup>. Based on the disturbance observer and self-triggered DMPC scheme, Yang <i>et al</i>. similarly achieved the collaborative control of nonlinear MASs<sup>[<a href="#b59" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b59">59</a>]</sup>.</p></div><div id="s2-3-3" class="article-Section"><h4 >2.3.3 Network unreliability</h4><p class="">The agents interact with the physical environment, communicate local information, and update the information of their neighbors, which requires connectivity, reliability, and security of the communication networks. DMPC-based control methods also need to take network security issues into account. Velarde <i>et al</i>. proposed a resilient DMPC control strategy that considers insider attacks<sup>[<a href="#b60" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b60">60</a>]</sup>. Ananduta <i>et al</i>. introduced an iterative DMPC strategy to mitigate the effects of false data injection attacks<sup>[<a href="#b61" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b61">61</a>]</sup>. Many studies regard denial of service (DOS) attacks as a data loss problem for MASs. For example, Dai <i>et al</i>. proposed a resilient robust DMPC scheme based on an extended sequence transmission strategy to eliminate the adverse effects under DOS attacks<sup>[<a href="#b62" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b62">62</a>]</sup>, and Chen <i>et al</i>. designed a similar event-triggered DMPC scheme<sup>[<a href="#b63" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b63">63</a>]</sup>. Wei <i>et al</i>. proposed a novel scheme for detecting distributed attacks using the DMPC method to achieve consensus of linear MASs under adversarial attacks<sup>[<a href="#b64" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b64">64</a>]</sup>.</p><p class="">To address the vulnerability of network communication, Hahn <i>et al</i>. designed a robust DMPC scheme for affine dynamical subsystems under communication delays<sup>[<a href="#b65" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b65">65</a>]</sup>. Su <i>et al</i>. addressed the tracking consistency problem by designing a DMPC strategy for linear MASs affected by disturbance and time-varying communication delays<sup>[<a href="#b66" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b66">66</a>]</sup>. Wang <i>et al</i>. designed an event-triggered DMPC scheme to solve the cooperative control problem for MASs with disturbance, input delays, and communication delays<sup>[<a href="#b67" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b67">67</a>]</sup>. Franzè <i>et al</i>. used the concept of reachability analysis to solve the leader-follower formation control problem under the data loss conditions in MASs<sup>[<a href="#b68" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b68">68</a>]</sup>. Yang <i>et al</i>. utilized Bernoulli distribution to describe the packet loss phenomenon and selected the prediction horizon of MASs based on an event-triggered scheme to achieve cooperative control<sup>[<a href="#b69" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b69">69</a>]</sup>.</p></div></div></div><div id="s3" class="article-Section"><h2 >3. DMPC FOR UAVS</h2><p class="">UAVs have been widely adopted as an emerging technology due to their high flexibility, mobility, and ease of deployment<sup>[<a href="#b10" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b10">10</a>]</sup>. Given the uncertainty of UAV application scenarios and the complexity of target missions, it is often challenging for an individual UAV to meet evolving mission requirements. UAVs can be controlled in a distributed way, thus realizing that individuals collaborate to perceive the surrounding environment together and complete multiple complex tasks as a whole through information sharing, intelligent collaboration, and autonomous decision-making<sup>[<a href="#b70" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b70">70</a>,<a href="#b71" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b71">71</a>]</sup>. Current research demonstrates that, based on the communication links between UAVs, UAVs can rapidly and accurately perform complex tasks such as cooperative path planning, target exploration, and formation control. Additionally, in the military domain, UAVs play a crucial role in essential tasks such as reconnaissance and strikes<sup>[<a href="#b72" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b72">72</a>]</sup>. For instance, the U.S. Air Force announced the Small UAV System Flight Plan in 2016, strategically confirming the future value of small UAVs and clarifying the concept of UAV swarm operations<sup>[<a href="#b73" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b73">73</a>]</sup>, the importance of UAVs continues to grow.</p><p class="">The DMPC method has recently received much attention due to its excellent ability to handle constrained optimization problems and fast computational capability. However, the research on the application of DMPC to UAVs still needs to be completed. The following sections provide an overview of the application of DMPC to UAVs in three key areas: trajectory optimization, formation control, and collision avoidance. In addition, <a href="#Table1" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Table1">Table 1</a> summarizes the existing research on DMPC-based UAVs considering multi-mission scenarios.</p><div id="Table1" class="Figure-block"><div class="table-note"><span class="">Table 1</span><p class="">Research of DMPC-based UAVs considering multi-mission scenarios</p></div><div class="table-responsive article-table"><table class="a-table"><thead><tr><td align="left" style="class:table_top_border"><b>Research</b></td><td align="center" style="class:table_top_border"><b>Trajectory optimization</b></td><td align="center" style="class:table_top_border"><b>Formation control</b></td><td align="center" style="class:table_top_border"><b>Collision avoidance</b></td><td align="center" style="class:table_top_border"><b>Communication restrictions</b></td><td align="center" style="class:table_top_border"><b>Disturbance and fault</b></td></tr></thead><tbody><tr><td align="left" style="class:table_top_border2">Bo <i>et al</i>.<sup>[<a href="#b74" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b74">74</a>]</sup></td><td align="center" style="class:table_top_border2">√</td><td align="center" style="class:table_top_border2"></td><td align="center" style="class:table_top_border2">√</td><td align="center" style="class:table_top_border2"></td><td align="center" style="class:table_top_border2"></td></tr><tr><td align="left">Qi <i>et al</i>.<sup>[<a href="#b75" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b75">75</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td></tr><tr><td align="left">Yang <i>et al</i>.<sup>[<a href="#b76" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b76">76</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Hu <i>et al</i>.<sup>[<a href="#b77" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b77">77</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Yu <i>et al</i>.<sup>[<a href="#b78" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b78">78</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Gräfe <i>et al</i>.<sup>[<a href="#b79" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b79">79</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center">√</td></tr><tr><td align="left">Li <i>et al</i>.<sup>[<a href="#b80" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b80">80</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Zheng <i>et al</i>.<sup>[<a href="#b81" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b81">81</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Chai <i>et al</i>.<sup>[<a href="#b82" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b82">82</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td></tr><tr><td align="left">Richards <i>et al</i>.<sup>[<a href="#b83" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b83">83</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Zhang <i>et al</i>.<sup>[<a href="#b84" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b84">84</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Chi <i>et al</i>.<sup>[<a href="#b85" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b85">85</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Zhou <i>et al</i>.<sup>[<a href="#b86" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b86">86</a>]</sup></td><td align="center">√</td><td align="center">√</td><td align="center">√</td><td align="center">√</td><td align="center"></td></tr><tr><td align="left">Chen <i>et al</i>.<sup>[<a href="#b87" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b87">87</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center">√</td><td align="center"></td></tr><tr><td align="left">Wen <i>et al</i>.<sup>[<a href="#b88" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b88">88</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center"></td><td align="center">√</td></tr><tr><td align="left">Yuan <i>et al</i>.<sup>[<a href="#b89" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b89">89</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center">√</td></tr><tr><td align="left">Li <i>et al</i>.<sup>[<a href="#b90" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b90">90</a>]</sup></td><td align="center">√</td><td align="center">√</td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left">Niu <i>et al</i>.<sup>[<a href="#b91" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b91">91</a>]</sup></td><td align="center">√</td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td></tr><tr><td align="left">Sun <i>et al</i>.<sup>[<a href="#b92" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b92">92</a>]</sup></td><td align="center"></td><td align="center">√</td><td align="center">√</td><td align="center"></td><td align="center"></td></tr><tr><td align="left" style="class:table_bottom_border">Jiang <i>et al</i>.<sup>[<a href="#b93" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b93">93</a>]</sup></td><td align="center" style="class:table_bottom_border">√</td><td align="center" style="class:table_bottom_border"></td><td align="center" style="class:table_bottom_border">√</td><td align="center" style="class:table_bottom_border"></td><td align="center" style="class:table_bottom_border"></td></tr></tbody></table></div><div class="table_footer"><div class="table_footer_note"><p class="para">DMPC: Distributed model predictive control; UAVs: unmanned aerial vehicles.</p></div></div></div><div id="s3-1" class="article-Section"><h3 >3.1 Trajectory optimization</h3><p class="">When UAVs operate in coordination, optimizing their generated paths to enhance mission efficiency while reducing overall energy consumption is crucial. The DMPC method can find the optimal paths under environmental constraints based on its ability to minimize the cost function and deal with the constraints, so the use of the DMPC method to provide real-time solutions for UAVs has received more and more attention.</p><p class="">Bo <i>et al</i>. considered UAV kinematics and collision avoidance constraints to develop a trajectory planning strategy based on DMPC, which achieved better real-time performance and more optimal trajectories compared to traditional trajectory optimization methods<sup>[<a href="#b74" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b74">74</a>]</sup>. Qi <i>et al</i>. utilized the DMPC method as a framework to design tracking trajectory optimization for ground targets, and introduced the Nash game method in the optimization solution process, then verified the feasibility of the proposed scheme by simulation<sup>[<a href="#b75" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b75">75</a>]</sup>. Similarly, Yang <i>et al</i>. also designed an online trajectory planning strategy based on the DMPC method<sup>[<a href="#b76" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b76">76</a>]</sup>, and Lun <i>et al</i>. investigated the application of UAVs as communication relay nodes for maritime vessels, and simulations verified that the designed DMPC algorithm was able to optimize energy costs while achieving UAVs trajectory planning<sup>[<a href="#b94" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b94">94</a>]</sup>. The optimization problem designed by Ao <i>et al</i>. combined the A* algorithm with Nash optimization, significantly reducing the solution size of the optimization problem while ensuring high accuracy of the generated trajectories<sup>[<a href="#b95" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b95">95</a>]</sup>.</p><p class="">Most of the aforementioned DMPC methods focus on basic trajectory optimization, but more complex trajectory planning tasks must account for obstacles, dynamic target tracking, and other challenging scenarios. Hu <i>et al</i>. considered the movement of the target, obstacles obstructing the line of sight, and energy constraints of the UAVs, and designed a DMPC strategy that balances optimization and prioritization, and experimentally verified the effectiveness of the UAVs in tracking targets in urban environments<sup>[<a href="#b77" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b77">77</a>]</sup>. Yu <i>et al</i>. also considered real-time target tracking and combined the adaptive difference algorithm with Nash optimization, and the DMPC was globally optimized with the help of Nash optimization, which improved the accuracy of target tracking<sup>[<a href="#b78" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b78">78</a>]</sup>. Gräfe <i>et al</i>. reduced the computational complexity and network traffic required for the DMPC method based on an event-triggered scheme while ensuring the safety and reliability of the generated trajectories<sup>[<a href="#b79" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b79">79</a>]</sup>. Yin <i>et al</i>. used a DMPC method to generate trajectories to achieve a stable network connection between the UAVs and the ground control stations<sup>[<a href="#b96" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b96">96</a>]</sup>. Notably, Luis <i>et al</i>. utilized online DMPC to generate trajectories of small UAV swarms in real-time and efficiently compute non-collision trajectories in mission scenarios through an on-demand collision avoidance method. The proposed method was shown to reduce flight time by approximately 50% on average in UAV point-to-point transition missions compared to the buffered voronoi cells (BVC)-based collision avoidance method. Meanwhile, the activation function was designed to detect any interference to the UAV, and an event-triggered replanning-based strategy was also devised. The algorithms involved were finally applied to a range of solid UAVs, from 2 to 20, and simulations were conducted to verify the effectiveness of the algorithms under a variety of scenarios, including obstacle-free transitions and transition tasks with static obstacles<sup>[<a href="#b97" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b97">97</a>]</sup>. Another key research on DMPC is the aerial robot swarms designed by Soria <i>et al</i>., whose objective functions included separation, propulsion, direction, and control. The quadrotor adjusted its flight trajectory based on interactive information, and the practical experiments with five quadrotors successfully demonstrated the safe flight of multiple drones in complex environments<sup>[<a href="#b98" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b98">98</a>]</sup>.</p><p class="">The search task, as a critical operation often performed by UAVs, is closely related to trajectory optimization. It is essential to ensure that the generated trajectories can effectively cover search areas while reducing energy consumption to meet various mission requirements in real-time. The DMPC-based search trajectory generation has been studied in some literature. Du <i>et al</i>. and Yao <i>et al</i>. developed UAV search trajectory optimization strategies by combining graph theory<sup>[<a href="#b99" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b99">99</a>]</sup> and target probabilistic graph<sup>[<a href="#b100" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b100">100</a>]</sup> under the DMPC framework, respectively. Trajectory optimization becomes particularly challenging in complex environments with unknown obstacles and communication interference. Hence, Li <i>et al</i>. proposed an adaptive guidance DMPC method to reduce exploration loss and improve exploration efficiency<sup>[<a href="#b80" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b80">80</a>]</sup>. Chai <i>et al</i>. used Voronoi diagrams to replan the search trajectory in real-time, avoiding the collision between repeated search and UAVs, and still achieved better performance in communication-constrained environments<sup>[<a href="#b82" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b82">82</a>]</sup>. It is worth mentioning that Zheng <i>et al</i>. applied DMPC to UAV collaborative area search by taking the neighbor prediction path as a parameter and distributing the overall search objective function in the constraints between UAVs<sup>[<a href="#b81" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b81">81</a>]</sup>. Simulation results demonstrated that their algorithm effectively improves search efficiency and verifies the scalability as the number of UAVs increased from 8 to 20.</p></div><div id="s3-2" class="article-Section"><h3 >3.2 Formation control</h3><p class="">The importance of UAV formation control lies in its ability to enhance mission efficiency and execute tasks such as search, surveillance, and rescue through coordinated formation. Maintaining formation also ensures safe distances between UAVs, safeguarding their operational safety. Research on UAV formation control using the DMPC method began with Richards <i>et al</i>. in 2004, who proposed a robust DMPC scheme for cooperative UAVs that avoided collisions by satisfying robust constraints. This strategy was significantly less computationally expensive than centralized algorithms and achieved superior tracking control performance<sup>[<a href="#b83" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b83">83</a>]</sup>. Subsequently, Ru <i>et al</i>. achieved formation reconfiguration control based on UAVs with different missions, using multi-objective game theory combined with the DMPC method to realize autonomous formation reconfiguration<sup>[<a href="#b101" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b101">101</a>]</sup>. Based on the DMPC framework, Bian <i>et al</i>. proposed an algorithm for fast formation control of UAVs on circular trajectories, effectively improving the convergence ability of the formation with lower computational consumption<sup>[<a href="#b102" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b102">102</a>]</sup>.</p><p class="">In addition, formation flight in complex situations is widely concerned; considering the different tasks of heterogeneous UAV formation and collision avoidance in formation movement, Zhang <i>et al</i>. designed a DMPC scheme based on adaptive differential evolution<sup>[<a href="#b84" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b84">84</a>]</sup>; Zhao <i>et al</i>. designed cost functions for leader, coordinator and follower UAVs, respectively, in heterogeneous UAVs, and simulations verified the feasibility of the designed DMPC strategies under the tasks of formation and retention, and insertion of new UAVs into the formation<sup>[<a href="#b103" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b103">103</a>]</sup>. Chi <i>et al</i>. achieved safe UAV formations using the particle swarm optimization (PSO) algorithm combined with the DMPC method<sup>[<a href="#b85" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b85">85</a>]</sup>, while Liu <i>et al</i>. realized rapid formation and maintenance of UAVs based on the DMPC method, demonstrating both stability and feasibility<sup>[<a href="#b104" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b104">104</a>]</sup>. For military applications, formation reconfiguration plays an essential role in performing military missions, such as attacking enemy military targets and searching for targets; Zhou <i>et al</i>. used the DMPC method while considering communication constraints to achieve UAVs that break through defenses under stealthy conditions<sup>[<a href="#b86" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b86">86</a>]</sup>. Another related and intriguing issue is collaborative payload transportation. For instance, Wehbeh <i>et al</i>. designed a system model connecting quadcopters with payloads and compared centralized MPC and DMPC schemes<sup>[<a href="#b105" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b105">105</a>]</sup>. Simulation experiments proved the effectiveness of the designed algorithm.</p><p class="">Recently, as DMPC has been more widely utilized in UAV formation control, existing studies have begun to consider the constraints of objective factors previously neglected in the literature, such as the limitations of the communication network, external disturbance, and errors due to model inaccuracies. Considering the actual situations of communication failure, Chen <i>et al</i>. designed a formation control algorithm based on relative position information about the relative distances and angles between UAVs, and then realized formation control based on the DMPC method in the presence of communication disturbances and information inaccuracies<sup>[<a href="#b87" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b87">87</a>]</sup>. Wen <i>et al</i>. designed a two-layer MPC scheme for UAVs, where the outer layer used a DMPC strategy to generate optimal control vectors, which combined with the inner layer's tube-based MPC, reduced control errors in UAV formation subjected to disturbance<sup>[<a href="#b88" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b88">88</a>]</sup>. Yuan <i>et al</i>. proposed a DMPC-based data transmission structure to accelerate the convergence of a six-degree-of-freedom UAV formation, with simulations employing data transmission delays following a Gaussian distribution<sup>[<a href="#b89" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b89">89</a>]</sup>. The designed unidirectional structure was shown to play a crucial role in system convergence, demonstrating the applicability of the proposed DMPC algorithm.</p><p class="">Encirclement is a tactic used to restrict a target by changing the formation of a group of UAVs. Its purpose is to maintain surveillance and prevent enemy targets from escaping or to protect friendly targets<sup>[<a href="#b106" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b106">106</a>]</sup>, and the process of encirclement can be viewed as a process of formation change and maintenance. Marasco <i>et al</i>. developed a strategy to encircle both moving and static targets using a circular formation based on the DMPC method<sup>[<a href="#b107" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b107">107</a>]</sup>. Based on the designed DMPC algorithm, Hafez <i>et al</i>. first considered the task allocation strategy in the UAVs in the simulation by estimating the trajectory cost of the target and minimizing the task time. The encirclement effect demonstrated the effectiveness of two UAV teams in encircling stationary and moving targets<sup>[<a href="#b108" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b108">108</a>]</sup>.</p></div><div id="s3-3" class="article-Section"><h3 >3.3 Collision avoidance</h3><p class="">When UAVs perform trajectory optimization and formation control, constructing a safe flight trajectory is fundamental to achieving cooperative control. Effective collision avoidance strategies can ensure that UAVs do not collide with obstacles and other aircraft, thus ensuring the integrity of the equipment, reducing the probability of accidents, and improving mission efficiency<sup>[<a href="#b109" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b109">109</a>]</sup>.</p><p class="">In previous research, such as that by Richards <i>et al</i>.<sup>[<a href="#b83" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b83">83</a>]</sup>, Bo <i>et al</i>.<sup>[<a href="#b74" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b74">74</a>]</sup>, and Zhang <i>et al</i>.<sup>[<a href="#b84" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b84">84</a>]</sup>, when optimizing trajectories and maintaining UAV formations based on the DMPC method, the safety of the formation was ensured by imposing safety or collision avoidance constraints. In addition, Li <i>et al</i>. addressed the collision problem at a low cost by designing a collision management unit and designing cooperative collision avoidance rules based on angle changes<sup>[<a href="#b90" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b90">90</a>]</sup>. It is worth mentioning that D'Amato <i>et al</i>. designed an MPC-based collision avoidance system and incorporated the right-of-way rules from the International Civil Aviation Organization (ICAO) to make UAV behavior predictable and compatible with human decision-making. The prediction unit was designed to predict potential collisions and calculate the required constraints, and the simulation results verify the effectiveness and scalability of their scheme<sup>[<a href="#b110" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b110">110</a>]</sup>.</p><p class="">Niu <i>et al</i>. designed UAVs to predict the motion trajectories of their neighbors to avoid collisions in situations where communication was impossible, demonstrating the effectiveness of the proposed scheme in scenarios involving no communication and multiple obstacles<sup>[<a href="#b91" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b91">91</a>]</sup>, Sun <i>et al</i>. also adopted a similar approach and employed the improved Quatre algorithm to enhance the stability of UAV formation<sup>[<a href="#b92" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b92">92</a>]</sup>. Jiang <i>et al</i>. developed a terminal condition to satisfy the collision avoidance algorithm for DMPC-based UAV formation control, aiming to reduce the conservatism of collision-free safe trajectories<sup>[<a href="#b93" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b93">93</a>]</sup>.</p></div></div><div id="s4" class="article-Section"><h2 >4. DMPC FOR VEHICLE PLATOONS</h2><p class="">Ground vehicles are common tools of transportation and play a significant role in people's lives. With the rapid development of sensors, control systems, and computer technology, expectations for vehicle performance have risen. Research on ground vehicles has focused on AGV platoons due to their potential to reduce traffic congestion, improve traffic efficiency, enhance vehicle safety, and save energy<sup>[<a href="#b20" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b20">20</a>,<a href="#b111" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b111">111</a>]</sup>. The effectiveness of vehicle platoons in maintaining safety and saving fuel has been experimentally demonstrated by the PATH program in California<sup>[<a href="#b112" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b112">112</a>]</sup>, the Energy ITS program in Japan<sup>[<a href="#b113" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b113">113</a>]</sup>, and the GCDC program in the Netherlands <sup>[<a href="#b114" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b114">114</a>]</sup>.</p><p class="">The primary objective of a vehicle platoon is to synchronize the movement of a group of vehicles by assigning a control role to each vehicle and exchanging information between vehicles to ensure that appropriate safety distances are maintained between adjacent vehicles<sup>[<a href="#b111" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b111">111</a>]</sup>. However, this method has limitations that make it challenging to maintain a stable platoon. The advancement of communication technology enables vehicles in a platoon to communicate through wireless or self-organizing networks. This facilitates the design of effective collaborative control strategies, improving the stability and efficiency of the platoon while ensuring smooth cooperative control and operation. <a href="#Figure5" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure5">Figure 5</a> shows four typical communication methods used in vehicle platoons of a front vehicle <inline-formula><tex-math id="M27">$$ 0 $$</tex-math></inline-formula> and <inline-formula><tex-math id="M28">$$ N $$</tex-math></inline-formula> rear vehicles<sup>[<a href="#b115" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b115">115</a>]</sup>. In addition, all of these communication topologies shown in <a href="#Figure5" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="Figure5">Figure 5</a> can be converted to unidirectional communication.</p><div class="Figure-block" id="Figure5"><div xmlns="http://www.w3.org/1999/xhtml" class="article-figure-image"><a href="/articles/ir.2024.19/image/Figure5" class="Article-img" alt="" target="_blank"><img alt="Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review" src="https://image.oaes.cc/e7dd7fcd-3c45-4298-b9e2-ec23a759ec19/ir4019-5.jpg" class="" title="" alt="" /></a></div><div class="article-figure-note"><p class="figure-note"></p><p class="figure-note">Figure 5. The directed communication topologies used in vehicle platoon. (A) PF topology; (B) PLF topology; (C) TPF topology; (D) TPLF topology. PF: Predecessor-following; PLF: predecessor-leader following; TPF: two-predecessor following; TPLF: two-predecessor-leader following.</p></div></div><p class="">Considering a vehicle platoon with a leader, the objective of the platooning is for each following vehicle <inline-formula><tex-math id="M29">$$ i $$</tex-math></inline-formula> to maintain an appropriate distance from the follower vehicles and the leader vehicle while following the leader at a speed of <inline-formula><tex-math id="M30">$$ v_0 $$</tex-math></inline-formula>. This objective can be given mathematically as:</p><p class=""><div class="disp-formula"><label>(4)</label><tex-math id="E4"> $$ \begin{align} \left\{ \begin{array}{ll} \lim_{t \rightarrow \infty}||v_i(t)-v_0(t)||=0\\ \lim_{t \rightarrow \infty}||s_{i-1}(t)-s_i(t)-d_{i-1, i}||=0\\ \lim_{t \rightarrow \infty}||s_i(t)-s_0(t)-d_0||=0\\ \end{array} \right. \end{align} $$ </tex-math></div></p><p class="">where <inline-formula><tex-math id="M31">$$ d_{i-1, i} $$</tex-math></inline-formula> is the desired distance between neighboring vehicles, and <inline-formula><tex-math id="M32">$$ d_0 $$</tex-math></inline-formula> is the desired distance between a follower vehicle and the leader vehicle. To control vehicle platoon using the DMPC scheme, local information interaction at each vehicle node is required. This approach achieves collaborative motion globally while adhering to the constraints outlined in Equation (4).</p><div id="s4-1" class="article-Section"><h3 >4.1 Strategy for platooning</h3><p class="">In the DMPC scheme, distributed controllers are deployed in each vehicle to collaborate in solving the constrained optimal control problem (COCP) for platooning over a finite time horizon and to exchange information via vehicle-to-vehicle communication links.</p><p class="">Maxim <i>et al</i>. set the constant speed of the leader and established the control strategy for the remaining vehicles; each vehicle was controlled by the DMPC method<sup>[<a href="#b116" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b116">116</a>]</sup>. Lu <i>et al</i>. demonstrated the stability of vehicle platoon under unidirectional communication topology for heterogeneous vehicles by designing a cost function based on the difference between the states of a vehicle and its neighboring vehicles<sup>[<a href="#b117" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b117">117</a>]</sup>. Similarly, Ma <i>et al</i>. achieved stable control of heterogeneous vehicles using an output feedback-based DMPC strategy<sup>[<a href="#b118" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b118">118</a>]</sup>. Zheng <i>et al</i>. presented the trajectory error-based cost functions for heterogeneous vehicles with dynamic coupling; this design ensured stability through equality-based terminal constraints subject to spatial geometric constraints<sup>[<a href="#b115" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b115">115</a>]</sup>; similar studies have appeared in the research of Qiang <i>et al</i>., they designed a two-layer control architecture, using vehicles with odd numbers as the first layer, sending information to vehicles with even numbers, and ensuring the distance and same speed of vehicles through sequential calculation<sup>[<a href="#b119" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b119">119</a>]</sup>. In addition, Yu <i>et al</i>. considered using the Nash optimal DMPC algorithm for platooning, which employed the Nash optimal algorithm to solve the decentralized problem and achieve Nash equilibrium for all vehicles<sup>[<a href="#b120" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b120">120</a>]</sup>. To keep the required control rate at the same level as the communication rate, Liu <i>et al</i>. proposed a non-iterative DMPC scheme for vehicle platooning, which ensured the stability of the closed-loop system through the linear matrix inequality technique and had compatibility constraints between the neighboring vehicles<sup>[<a href="#b121" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b121">121</a>]</sup>. The simulation verified the effective control of the vehicle platooning in the presence of joining and leaving vehicles.</p><p class="">Similar to the factors to be considered by DMPC in UAVs, computational resources and computational speed determine the ability of the vehicle platoon to deal with emergencies quickly. To solve the problem of shortage of computational resources, Bai <i>et al</i>. designed a parallel DMPC method based on the ADMM, which used the Lagrange multiplier method and the dual decomposition technique<sup>[<a href="#b122" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b122">122</a>]</sup>. For a mixed fleet of autonomous vehicles and human-driven vehicles, Zhan <i>et al</i>. proposed the ADMM-based DMPC method to obtain the global optimal solution of the local controller for the sub-platoons, which significantly reduced the computational consumption<sup>[<a href="#b123" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b123">123</a>]</sup>.</p><p class="">To operate vehicle platoons on real roads, it is essential to account for the fact that the speed of the leader vehicle is time-varying to adapt to the road conditions. To address this problem, Maxim <i>et al</i>. proposed a DMPC method for tracking the leader vehicle<sup>[<a href="#b124" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b124">124</a>]</sup>. On the other hand, Yan <i>et al</i>. analyzed the stability and feasibility of the DMPC method for vehicle platooning systems<sup>[<a href="#b125" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b125">125</a>]</sup>. Qiang <i>et al</i>. addressed the problem of coupled state vehicles with distance constraints and cost functions, which computed the state-coupled set for decoupling constraints and solved the DMPC optimization problem when the information of the leader vehicle is unknown<sup>[<a href="#b126" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b126">126</a>]</sup>. Simulation results demonstrated that the proposed algorithm can ensure stable tracking between vehicles even when the lead vehicle has variable inputs.</p></div><div id="s4-2" class="article-Section"><h3 >4.2 Robustness of platooning</h3><p class="">Most research on DMPC-based vehicle platoon control assumes an accurate model. However, model uncertainty, sensor noise, and environmental disturbances can adversely affect the accuracy of the DMPC scheme. Additionally, communication delays and data transmission losses during vehicle-to-vehicle information exchange can further degrade platooning performance. Therefore, robust DMPC schemes should be developed to maintain system stability under these uncertainties.</p><p class="">Luo <i>et al</i>. addressed the problem of disturbances and modeling errors in vehicle platoon systems, employing the proportional multiple integral (PMI) observer techniques with unknown inputs to limit the deviation between the actual systems and nominal systems<sup>[<a href="#b127" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b127">127</a>]</sup>. For the same situation, Ju <i>et al</i>. also proposed a stochastic DMPC scheme and verified the effectiveness of the control scheme in the presence of model uncertainties<sup>[<a href="#b128" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b128">128</a>]</sup>; Yin <i>et al</i>. combined Taguchi's robustness with stochastic DMPC scheme to reduce the negative impact of uncertainty on the performance of platooning<sup>[<a href="#b129" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b129">129</a>]</sup>. For the vehicle platoon systems subjected only to additive disturbances, Luo <i>et al</i>. proposed a robust DMPC scheme for tracking virtual time-varying trajectories for non-complete vehicle platoon systems<sup>[<a href="#b130" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b130">130</a>]</sup>, and Chen <i>et al</i>. utilized local and neighbor uncertainty distribution information to collaboratively handle coupled probabilistic constraints in vehicle platoon systems. Based on the designed self-triggered mechanism, a constraint tightening strategy was implemented in the optimization problem to ensure the stability of the systems at the triggering moment. Simulation experiments were also conducted in a vehicle platoon system with five vehicles to verify the effectiveness of the algorithm in the case of queue control and emergency braking<sup>[<a href="#b131" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b131">131</a>]</sup>. In addition, Mousavi <i>et al</i>. considered uncertain resources in dynamic environments, incorporating the evolution of vehicles and the environment into the planning strategy, resulting in a general framework consisting of estimation, prediction, and planning<sup>[<a href="#b132" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b132">132</a>]</sup>.</p><p class="">In recent years, research has increasingly focused on data-driven approaches to effectively address inaccuracies in modeling heterogeneous vehicle platoon systems. The basic principle of data-driven modeling is to use the input and output data of the system to construct the system model, and data-driven DMPC methods have been recently investigated by Huang <i>et al</i>.<sup>[<a href="#b133" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b133">133</a>]</sup>, Zheng <i>et al</i>.<sup>[<a href="#b134" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b134">134</a>]</sup> and Kohler <i>et al</i><sup>[<a href="#b135" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b135">135</a>]</sup>. The basic principle of data-driven modeling is to use the input and output data of the system to construct the system model, and data-driven DMPC methods have been recently investigated by Zheng <i>et al</i>.<sup>[<a href="#b134" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b134">134</a>]</sup> and Kohler <i>et al</i>.<sup>[<a href="#b135" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b135">135</a>]</sup>. Based on this method, Huang <i>et al</i>. added a variable for estimating the global consensus distributed across each agent in the optimization problem and actively compensated for the communication delay based on input-output data. The simulation results demonstrated the convergence of the auxiliary variables with the system output, verifying the effectiveness of the designed algorithm under communication delay<sup>[<a href="#b133" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b133">133</a>]</sup>. Wu <i>et al</i>. established a data-driven model using subspace identification for a heterogeneous vehicle platoon to achieve stability under the DMPC method<sup>[<a href="#b136" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b136">136</a>]</sup>. It is worth mentioning that Zhan <i>et al</i>. mapped the nonlinear model to a high-dimensional linear space based on the theory of the Koopman operator, and designed a neural network framework based on extended dynamic mode decomposition (EDMD) to approximate the Koopman operator. The simulation experiment used 25 vehicles, and the centralized MPC and DMPC methods were used, respectively. The results showed that DMPC can reduce the computational cost. The method has a faster convergence speed than the traditional nonlinear DMPC method<sup>[<a href="#b137" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b137">137</a>]</sup>.</p><p class="">When data losses occur during the communication of vehicle platoons, such as packet losses and communication delays, it is crucial for vehicle platoon control to estimate the lost data and accurately continue the mission. Wang <i>et al</i>. addressed data estimation under packet loss by designing a DMPC scheme that solves invariant sets and feedback control laws<sup>[<a href="#b67" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b67">67</a>]</sup>. Pauca <i>et al</i>. used the information received by the vehicle at the previous moment to alleviate packet losses caused by wireless communication networks that exchanged information between vehicles<sup>[<a href="#b138" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b138">138</a>]</sup>. In scenarios where inter-vehicle communication is limited and communication delays exist, Xu <i>et al</i>. used buffers and delay compensators to reduce the interference caused by non-ideal communication<sup>[<a href="#b139" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b139">139</a>]</sup>. Wang <i>et al</i>. designed an event-triggered scheme based on state errors and input delays and proposed a compensation scheme for input and communication delays<sup>[<a href="#b67" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b67">67</a>]</sup>. Similarly, Maxim <i>et al</i>. and Yan <i>et al</i>. designed DMPC schemes to achieve stable control of vehicle platoons in the presence of time-varying communication delays<sup>[<a href="#b124" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b124">124</a>,<a href="#b125" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b125">125</a>]</sup>.</p></div><div id="s4-3" class="article-Section"><h3 >4.3 Security of platooning</h3><p class="">When a vehicle platoon is traveling on a roadway, preventing collisions is paramount to ensuring passenger safety, and recent research has focused on enhancing the safety of vehicle platoons. Mohseni <i>et al</i>. considered the non-holonomic property of the vehicle platoons while predicting the behavior of other vehicles, and designed a cooperative DMPC scheme with predictive collision avoidance features to ensure collision avoidance even when the vehicle deviates from the desired trajectory<sup>[<a href="#b140" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b140">140</a>]</sup>. Liu <i>et al</i>. considered the interactions between vehicles and their neighbors, and by analyzing the data of expressway naturalistic driving, the authors summarized the characteristics from aggressive driving behaviors to cautious driving behaviors, and designed collaborative strategies for different driving behaviors. Notably, the proposed DMPC scheme was validated through hardware-in-the-loop simulation, demonstrating its ability to safely perform tasks such as following a vehicle and changing lanes in high-risk situations<sup>[<a href="#b141" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b141">141</a>]</sup>. In addition, the safe merging problem of heterogeneous vehicle platoons is studied by Liu <i>et al</i>.<sup>[<a href="#b141" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b141">141</a>]</sup>. By designing the collision safety constraints, Gratzer <i>et al</i>. ensured the stability of the vehicle platoon during sudden braking maneuvers<sup>[<a href="#b142" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b142">142</a>]</sup>. In the research of Franzè <i>et al</i>., vehicle platoons could flexibly adjust their topologies in the presence of obstacles, thus ensuring the safe operation of the systems<sup>[<a href="#b143" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b143">143</a>]</sup>.</p><p class="">Ensuring network security is also crucial for vehicle platoons, as vehicle-to-vehicle information transmission is vulnerable to malicious intrusions and cyber-attacks, which can threaten the stability of the platoon and potentially lead to human injury and property loss. Chen <i>et al</i>. established a dynamic event triggering scheme with DoS attack sensing capability, where the event triggering threshold was adjusted according to the DoS attack duration and vehicle states. The evolution of vehicle positions, spacing, and speeds in the formation under different event-triggering parameters and DoS attack durations were verified through simulation, demonstrating the resilience and reliability of the designed DMPC algorithm in addressing security challenges<sup>[<a href="#b144" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b144">144</a>]</sup>. Lyu <i>et al</i>. designed a communication topology safety response system that incorporates the DMPC method and demonstrates that it can effectively ensure the stability and security of the vehicle platoons under cyber-attacks<sup>[<a href="#b145" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b145">145</a>]</sup>. Zeng <i>et al</i>. developed a resilient DMPC framework for vehicle platoons under Byzantine attacks, which detected unreliable information based on the resilient set and previously transmitted information, and achieved excellent performance with guaranteed safety<sup>[<a href="#b146" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b146">146</a>]</sup>.</p></div></div><div id="s5" class="article-Section"><h2 >5. CHALLENGES AND FUTURE</h2><p class="">The previous sections reviewed the application of DMPC methods in UAVs and vehicle platoon systems, but significant theoretical and implementation challenges remain. This section summarizes the challenges and future of DMPC methods in practical application.</p><div id="s5-1" class="article-Section"><h3 >5.1 Security control</h3><p class="">The DMPC method has shown great potential in UAVs and vehicle platoon systems, but its safety issues cannot be ignored. Due to the dependence of DMPC on network physical systems, there is a risk of nonmalicious failures, such as communication delays and data loss, which may lead to system instability. In addition, the distributed nature of DMPC makes it vulnerable to network attacks, especially deception attacks<sup>[<a href="#b147" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b147">147</a>,<a href="#b148" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b148">148</a>]</sup> and interrupt attacks<sup>[<a href="#b149" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b149">149</a>]</sup>. Attackers can tamper with control signals or disrupt communication networks, seriously affecting system performance and potentially causing recursive feasibility and stability issues.</p><p class="">To address these security challenges, researchers have proposed various network security control methods and fault tolerant control (FTC) technologies. These approaches are designed to maintain system stability by detecting, identifying, and mitigating the effects of network attacks. For example, a design based on robust DMPC can improve the security margin of the system in the face of network attacks, ensuring the integrity of input signals<sup>[<a href="#b144" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b144">144</a>]</sup>. In addition, the FTC method mitigates security issues caused by malicious agents by actively isolating faulty subsystems<sup>[<a href="#b150" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b150">150</a>]</sup>. In Section 4.3 of the previous text, a brief statement was made regarding the network communication security control issues of vehicle platoon systems. However, the security control issues of UAVs and vehicle platoon systems based on DMPC still require further research. In recent years, emerging technologies such as cloud computing and blockchain have also demonstrated the potential to enhance the security of DMPC<sup>[<a href="#b151" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b151">151</a>,<a href="#b152" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b152">152</a>]</sup>. The cloud-based MPC framework can utilize encryption technology to keep data encrypted during transmission and processing, thereby preventing data leakage and attacks<sup>[<a href="#b153" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b153">153</a>]</sup>. Meanwhile, blockchain technology has the potential to provide a secure distributed information exchange platform for MASs, thereby further enhancing the ability of the system to resist attacks<sup>[<a href="#b154" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b154">154</a>]</sup>. In the future, the development of DMPC methods will rely on the combination of stronger network defense mechanisms and FTC methods. The incorporation of cutting-edge technologies such as cloud computing and blockchain will be critical in developing more secure and resilient distributed control systems, particularly for applications with stringent security requirements, such as UAVs and vehicle platoon systems.</p></div><div id="s5-2" class="article-Section"><h3 >5.2 Data-driven control</h3><p class="">Most of the existing DMPC methods are based on accurate system models, but considering the difficulty in obtaining models in actual systems or the use of imprecise and unstable models, there are significant differences between theoretical and actual results. Data-driven control, by contrast, is a method that does not depend on an exact system model. It generates control inputs through a designed algorithm based on data obtained by the system over a period of historical time, which can solve the current problem of DMPC relying on an exact model. Kohler <i>et al</i>. designed a linear data-driven DMPC scheme with dynamic coupling features based on Willems' Fundamental Lemma <sup>[<a href="#b135" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b135">135</a>,<a href="#b155" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b155">155</a>]</sup>. Additionally, researchers have proposed scalable data-driven DMPC schemes<sup>[<a href="#b156" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b156">156</a>]</sup> for large-scale systems, dissipative behavior-based data-driven DMPC schemes<sup>[<a href="#b157" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b157">157</a>]</sup>, and data-driven DMPC schemes for direct current (DC) microgrids<sup>[<a href="#b158" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b158">158</a>]</sup> and complex traffic network management<sup>[<a href="#b159" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b159">159</a>]</sup>. In addition, Fawcett <i>et al</i>. successfully achieved robust motion control of quadruped robots in complex environments by combining behavioral system theory with distributed data-driven predictive control technology<sup>[<a href="#b160" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b160">160</a>]</sup>, which demonstrated the effectiveness of data-driven methods in different systems. As noted earlier, the application of data-driven DMPC in vehicle exhaust systems to handle solutions with uncertain dynamics has gained significant attention<sup>[<a href="#b136" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b136">136</a>,<a href="#b137" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b137">137</a>]</sup>. In summary, data-driven DMPC has shown outstanding performance in handling dynamic responses and optimizing control of unknown complex systems, demonstrating its extensive potential and development prospects in multiple fields. However, in current data-driven DMPC research, how to ensure that robust data-driven DMPC methods can be obtained even if the data is unreliable or partially missing still needs to be studied.</p><p class="">In addition to traditional data-driven DMPC control schemes, there is growing interest in data-driven DMPC approaches based on learning methods. Gros <i>et al</i>. demonstrated that reinforcement learning (RL) could achieve stable MPC control under model uncertainty and also studied the presence of disturbances<sup>[<a href="#b161" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b161">161</a>,<a href="#b162" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b162">162</a>]</sup>. Mallick <i>et al</i>. extended this work to MASs, implementing RL and deployment of DMPC as a function approximator<sup>[<a href="#b163" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b163">163</a>]</sup>. Similarly, Liu <i>et al</i>. designed a neural network-based DMPC approximator that successfully reduced the computational burden of DMPC in large-scale systems<sup>[<a href="#b164" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b164">164</a>]</sup>. Another learning-based approach utilizes deep learning, such as combining long short-term memory (LSTM) units with MPC schemes to reduce energy consumption<sup>[<a href="#b165" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b165">165</a>]</sup>, using deep belief networks to find the optimal control list for MPC for sewage treatment <sup>[<a href="#b166" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b166">166</a>]</sup>, and combining autoencoders with MPC for automatic power generation control<sup>[<a href="#b167" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b167">167</a>]</sup>. Notably, Salzmann <i>et al</i>. implemented real-time onboard tracking control for quadcopters using deep learning and MPC<sup>[<a href="#b168" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b168">168</a>]</sup>. However, there have been limited achievements in combining DMPC schemes with deep learning. Yin <i>et al</i>. combined LSTM units with convolutional neural networks (CNN) for feature extraction and prediction of offshore wind farms, and then used DMPC for control<sup>[<a href="#b169" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b169">169</a>]</sup>. D'Alfonso <i>et al</i>. used deep RL combined with DMPC to achieve vehicle exhaust control<sup>[<a href="#b170" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b170">170</a>]</sup>. Given the powerful ability of deep learning to capture system features, especially in complex nonlinear and large-scale systems, its combination with DMPC can significantly enhance the dynamic modeling capability of the system. In the future, it is essential to focus on the computational efficiency and dynamic adaptability of data-driven DMPC solutions to enable their application in a broader range of scenarios, such as UAVs and vehicle platoon systems.</p></div><div id="s5-3" class="article-Section"><h3 >5.3 Practical limitations</h3><p class="">In addition to considering the theoretical challenges of DMPC, it is also crucial to address the practical challenges that arise during the implementation of DMPC in UAVs and vehicle exhaust systems. A primary challenge is hardware limitations, as actual system models are often nonlinear, requiring nonlinear model predictive control (NMPC) methods instead of linear MPC calculations in most cases. Compared to the most advanced non-predictive methods, NMPC imposes significantly higher computational demands, making it difficult to deal with the nonlinear optimization problems on vehicles and UAVs with limited processing power<sup>[<a href="#b171" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b171">171</a>]</sup>. This issue is more prominent in UAVs with more limited memory and computing resources. Additionally, some hardware components may impose further constraints on the construction of MPC problems, thereby affecting the feasibility of these problems. Some constraints require the design of DMPC strategies with higher computational efficiency and lower power consumption. With further development of hardware and nonlinear optimization solvers<sup>[<a href="#b172" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b172">172</a>,<a href="#b173" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b173">173</a>]</sup>, as well as computational research based on field programmable gate arrays (FPGA)<sup>[<a href="#b174" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b174">174</a>,<a href="#b175" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b175">175</a>]</sup> and microprocessors<sup>[<a href="#b176" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b176">176</a>]</sup>, running NMPC algorithm with nonlinear fully dynamic models on embedded computers has become easier to compute. However, obtaining more efficient solutions to reduce hardware limitations remains an open problem.</p><p class="">Communication delay presents another critical challenge. In distributed control systems, particularly in UAVs and vehicle platoon systems, effective communication is essential for coordination. Sections 2.4 and 4.2 in the previous text have discussed some situations where communication delays and packet loss occur in UAVs and vehicle platoon systems. Due to factors such as signal attenuation, channel congestion, and external radio interference, data transmission may be delayed or lost, which can degrade the performance of DMPC, leading to suboptimal control actions or even system instability, thereby jeopardizing the safety of the systems. Therefore, it is crucial to incorporate robust communication protocols and consider delay compensation techniques within the DMPC framework, and there have been numerous theoretical studies that have taken into account communication delays or packet loss situations<sup>[<a href="#b66" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b66">66</a>,<a href="#b67" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b67">67</a>,<a href="#b177" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b177">177</a>,<a href="#b178" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b178">178</a>]</sup>. However, in practical implementation, due to the limitations of hardware to some extent, few studies have verified the practical effectiveness of theoretical DMPC schemes through hardware-in-the-loop simulations<sup>[<a href="#b179" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b179">179</a>]</sup>. This issue merits further consideration in future research.</p><p class="">Environmental factors also play an essential role in the practical deployment of DMPC. Uncertain dynamic environments, such as constantly changing weather conditions, obstacles in forests or complex terrains, sudden road accidents, and occasional pedestrians in UAVs and vehicle platoon systems, present significant challenges to the safety and robustness of DMPC strategies. The DMPC strategy must be adaptable and resilient to possible uncertain situations to ensure safe and reliable operation in real-world scenarios. For MPC-based approaches, Lindqvist <i>et al</i>. proposed a method for UAVs to quickly handle dynamic obstacles. However, there are still limitations in relying on motion capture systems to detect obstacles clearly<sup>[<a href="#b180" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b180">180</a>]</sup>. Batkovic <i>et al</i>. designed the auto drive system for cycling based on the model predictive flexible trajectory tracking control (MPFTC) framework to deal with unforeseen road emergencies<sup>[<a href="#b181" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b181">181</a>]</sup>. In a distributed scenario, obstacle avoidance trajectory planning in complex environments for UAVs has been proposed <sup>[<a href="#b98" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b98">98</a>]</sup>. Additionally, scenario-based MPC methods have emerged as a potential solution to the challenges posed by changing environments<sup>[<a href="#b182" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b182">182</a>]</sup>, which can introduce factors such as terrain into the prediction range and adjust the control strategy in advance to maintain the system performance in changeable environment<sup>[<a href="#b183" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b183">183</a>]</sup>. Furthermore, methods based on machine learning<sup>[<a href="#b168" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b168">168</a>,<a href="#b184" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b184">184</a>]</sup> or RL<sup>[<a href="#b161" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b161">161</a>,<a href="#b185" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b185">185</a>]</sup> can make the system robust to dynamic environments through online learning and adaptive strategies, and also have the potential to be applied to participate in designing DMPC strategies in dynamic environments.</p><p class="">The design of DMPC performance parameters, such as the state weight matrix and control weight matrix, plays a crucial role in determining the effectiveness and efficiency of control strategies. These parameters significantly influence the behavior of the system, affecting its stability, robustness, and convergence speed. However, traditional methods for designing these parameters often rely on human expertise and intuition, introducing a degree of randomness and subjectivity into the algorithm implementation process. Although RL-based parameter update methods have demonstrated the ability to achieve desired control effects even with imprecise parameters<sup>[<a href="#b161" class="Link_style" data-jats-ref-type="bibr" data-jats-rid="b161">161</a>]</sup>, designing an adaptive parameter adjustment scheme suitable for different systems or using learning-based methods such as RL and neural networks to find better parameters and apply them well to practical systems is still worth further research.</p></div></div><div id="s6" class="article-Section"><h2 >6. CONCLUSIONS</h2><p class="">This paper reviews the application of DMPC methods in UAVs and vehicle platoon systems. These systems rely on communication to exchange information and coordinate tasks such as trajectory planning, formation control, and platoon control through DMPC methods. Additionally, considering the robustness and security of AIS, DMPC methods must address complex environmental constraints, external disturbances, and cyber-attacks. While there is a foundation of research on these issues, further investigation is needed to address more practical and complex mission scenarios. This paper also summarizes the challenges faced by existing DMPC methods in AIS. However, the work presented here has its limitations. The application examples provided in this paper aim to help readers understand current research directions and challenges, and to inform future work.</p></div><div id="s7" class="article-Section"><h2 >DECLARATIONS</h2><div id="s7-1" class="article-Section"><h3 >Authors' contributions</h3><p class="">Project administration: Yan H</p><p class="">Writing original draft: Peng Y</p><p class="">Commentary and critical review: Rao K, Yang P, Lv Y</p></div><div id="s7-2" class="article-Section"><h3 >Availability of data and materials</h3><p class="">Not applicable.</p></div><div id="s7-3" class="article-Section"><h3 >Financial support and sponsorship</h3><p class="">This work is supported by the National Natural Science Foundation of China (62333005) and the Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00105).</p></div><div id="s7-4" class="article-Section"><h3 >Conflicts of interest</h3><p class="">Yan H is an Editorial Board Member of the journal <i>Intelligence & Robotics</i> and the guest editor of the Special Issue "Robot System Intelligentization and Application: Learning, Control and Decision", while the other authors have declared that they have no conflicts of interest.</p></div><div id="s7-5" class="article-Section"><h3 >Ethical approval and consent to participate</h3><p class="">Not applicable.</p></div><div id="s7-6" class="article-Section"><h3 >Consent for publication</h3><p class="">Not applicable.</p></div><div id="s7-7" class="article-Section"><h3 >Copyright</h3><p class="">© The Author(s) 2024.</p></div></div></div> <!----> <div class="art_list" data-v-49c221b8></div> <div class="article_references" data-v-49c221b8><div class="ReferencesBox" data-v-49c221b8><h2 id="References" class="bg_d" data-v-49c221b8><span data-v-49c221b8><a href="/articles//reference" data-v-49c221b8>REFERENCES</a></span> <span class="icon" data-v-49c221b8><i class="el-icon-arrow-down" data-v-49c221b8></i> <i class="el-icon-arrow-up hidden" data-v-49c221b8></i></span></h2> <div class="references_list heightHide" data-v-49c221b8><div id="b1" class="references_item" data-v-49c221b8><p data-v-49c221b8><span data-v-49c221b8>1. </span> <span data-v-49c221b8>Aceto G, Persico V, Pescapé A. 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IEEE; 2023. pp. 507–14.</span></p> <div class="refrences" data-v-49c221b8><a href="https://dx.doi.org/10.1109/ICUAS57906.2023.10156232" target="_blank" data-v-49c221b8><button type="button" class="el-button el-button--text el-button--mini" data-v-49c221b8><!----><!----><span>DOI</span></button></a> <!----> <!----></div></div></div> <div class="line" data-v-49c221b8></div></div> <div class="article_cite cite_layout" data-v-49c221b8><div id="cite" data-v-49c221b8></div> <div class="el-row" style="margin-left:-10px;margin-right:-10px;" data-v-49c221b8><div class="el-col el-col-24 el-col-xs-24 el-col-sm-16" style="padding-left:10px;padding-right:10px;" data-v-49c221b8><div class="left_box" data-v-49c221b8><div data-v-49c221b8><h2 style="margin-top:0!important;padding-top:0;" data-v-49c221b8>Cite This Article</h2> <div class="cite_article" data-v-49c221b8><div class="cite_article_sec" data-v-49c221b8>Review</div> <div class="cite_article_open" style="color:#aa0c2f;" data-v-49c221b8><img src="https://g.oaes.cc/oae/nuxt/img/open_icon.bff5dde.png" alt="" style="width:10px;" data-v-49c221b8> Open Access</div> <div class="cite_article_tit" data-v-49c221b8><span data-v-49c221b8>Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review</span></div> <div class="cite_article_editor" data-v-49c221b8><span data-v-49c221b8>Yang Peng<a href='https://orcid.org/0009-0008-0113-850X' target='_blank'><img src='https://i.oaes.cc/images/orcid.png' class='author_id' alt='Yang Peng'></a>, ... 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Chemical Process of Ministry of Education, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China. E-mail: \u003Cemail\u003Ehcyan@ecust.edu.cn\u003C\u002Femail\u003E",editor:[],editor_time:"\u003Cspan\u003E\u003Cb\u003EReceived:\u003C\u002Fb\u003E 3 Apr 2024 | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003EFirst Decision:\u003C\u002Fb\u003E 1 Aug 2024 | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003ERevised:\u003C\u002Fb\u003E 5 Sep 2024 | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003EAccepted:\u003C\u002Fb\u003E 11 Sep 2024 | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003EPublished:\u003C\u002Fb\u003E 24 Sep 2024\u003C\u002Fspan\u003E",cop_link:"https:\u002F\u002Fcreativecommons.org\u002Flicenses\u002Fby\u002F4.0\u002F",cop_info:"© The Author(s) 2024. \u003Cb\u003EOpen Access\u003C\u002Fb\u003E This article is licensed under a Creative Commons Attribution 4.0 International License (\u003Ca target=\"_blank\"href=\"https:\u002F\u002Fcreativecommons.org\u002Flicenses\u002Fby\u002F4.0\u002F\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\"\u003Ehttps:\u002F\u002Fcreativecommons.org\u002Flicenses\u002Fby\u002F4.0\u002F\u003C\u002Fa\u003E), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.",keywords:["Distributed model predictive control","autonomous intelligent systems","multi-agent systems","unmanned aerial vehicles","vehicle platoon systems"],issue:U,image:"https:\u002F\u002Foaepublishstorage.blob.core.windows.net\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-coverimg.jpg",tag:" \u003Ci\u003EIntell Robot\u003C\u002Fi\u003E 2024;4(3):293-317.",authors:"Yang Peng\u003Ca href='https:\u002F\u002Forcid.org\u002F0009-0008-0113-850X' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Yang Peng'\u003E\u003C\u002Fa\u003E, ... Yunkai Lv\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0001-5212-8629' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Yunkai Lv'\u003E\u003C\u002Fa\u003E",picurl:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-coverimg.big.jpg",expicurl:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-coverimg.jpg",picabstract:f,interview_pic:f,interview_url:f,review:a,cop_statement:"© The Author(s) 2024.",seo:[],video_img:a,lpage:317,author:[{base:"Yang Peng\u003Csup\u003E\u003C\u002Fsup\u003E",email:a,orcid:"https:\u002F\u002Forcid.org\u002F0009-0008-0113-850X"},{base:"Huaicheng Yan\u003Csup\u003E\u003C\u002Fsup\u003E",email:a,orcid:"https:\u002F\u002Forcid.org\u002F0000-0001-5496-1809"},{base:"Kai Rao\u003Csup\u003E\u003C\u002Fsup\u003E",email:a,orcid:"https:\u002F\u002Forcid.org\u002F0000-0003-2520-3077"},{base:"Penghui Yang\u003Csup\u003E\u003C\u002Fsup\u003E",email:a,orcid:a},{base:"Yunkai Lv\u003Csup\u003E\u003C\u002Fsup\u003E",email:a,orcid:"https:\u002F\u002Forcid.org\u002F0000-0001-5212-8629"}],specialissue:{id:V,name:W},specialinfo:a,date_published_stamp:1727107200,year1:D,CitedImage:"https:\u002F\u002Fi.oaes.cc\u002Fimages_2018\u002Fjournals\u002FCrossref.png",article_editor:[],editoruser:"\u003Cspan\u003E\u003Cb\u003EAcademic Editor:\u003C\u002Fb\u003E Simon X. Yang | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003ECopy Editor:\u003C\u002Fb\u003E Pei-Yun Wang | \u003C\u002Fspan\u003E\u003Cspan\u003E\u003Cb\u003EProduction Editor:\u003C\u002Fb\u003E Pei-Yun Wang\u003C\u002Fspan\u003E",commentsNums:d,oaestyle:X,amastyle:Y,ctstyle:Z,acstyle:_,copyImage:"https:\u002F\u002Fi.oaes.cc\u002Fimages_2018\u002Fjournals\u002Fccb_4.png",affiliation:[{id:99686,article_id:b,Content:"\u003Clabel\u003E\u003C\u002Flabel\u003E\u003Caddr-line\u003EKey Laboratory of Smart Manufacturing in Energy Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China. \u003C\u002Faddr-line\u003E"}],related:[{article_id:E,journal_id:r,section_id:i,path:n,journal:o,ar_title:F,date_published:$,doi:G,author:[{first_name:aa,middle_name:a,last_name:ab,ans:g,email:ac,bio:a,photoUrl:a},{first_name:ad,middle_name:a,last_name:ae,ans:g,email:a,bio:a,photoUrl:a},{first_name:af,middle_name:a,last_name:ag,ans:g,email:a,bio:a,photoUrl:a},{first_name:ah,middle_name:a,last_name:ai,ans:g,email:a,bio:a,photoUrl:a}]},{article_id:H,journal_id:r,section_id:i,path:n,journal:o,ar_title:I,date_published:aj,doi:J,author:[{first_name:v,middle_name:a,last_name:ak,ans:g,email:a,bio:a,photoUrl:a},{first_name:al,middle_name:a,last_name:am,ans:an,email:ao,bio:a,photoUrl:a},{first_name:ap,middle_name:a,last_name:w,ans:g,email:a,bio:a,photoUrl:a},{first_name:aq,middle_name:a,last_name:ar,ans:x,email:a,bio:a,photoUrl:a}]},{article_id:K,journal_id:r,section_id:i,path:n,journal:o,ar_title:L,date_published:as,doi:M,author:[{first_name:at,middle_name:a,last_name:au,ans:g,email:a,bio:a,photoUrl:a},{first_name:v,middle_name:a,last_name:w,ans:g,email:av,bio:a,photoUrl:a},{first_name:aw,middle_name:a,last_name:ax,ans:g,email:a,bio:a,photoUrl:a},{first_name:ay,middle_name:a,last_name:az,ans:x,email:a,bio:a,photoUrl:a}]}],down:"https:\u002F\u002Ff.oaes.cc\u002Fris\u002F7201.ris",xml:{id:5289,article_id:b,xml_down:d,cite_click:d,export_click:d},zan:d,cited_type:"cited",subarray:[],issn:"ISSN 2770-3541 (Online)",uuid:"7658793235017daa001afca646e0f274",abstractUuid:"1aaa161e7b8339623ed9db10799dc423",apiurl:a,api_abstract_url:a,journal_id:aA,journal_path:n},loadingAbs:void 0,loading:u,ArtDataC:{content:"\u003Cdiv id=\"s1\" class=\"article-Section\"\u003E\u003Ch2 \u003E1. INTRODUCTION\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EWith the rapid development of communication technology and computer science, the deep integration of complex systems and sensing decision-making has gained unprecedented development\u003Csup\u003E[\u003Ca href=\"#b1\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b1\"\u003E1\u003C\u002Fa\u003E,\u003Ca href=\"#b2\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b2\"\u003E2\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Autonomous intelligent systems (AIS) are capable of environmental sensing, target detection, and cooperative control through the integration of advanced control, communication modules, and sensing technologies. They have the ability to autonomously plan actions, share resources, and operate remotely to complete tasks\u003Csup\u003E[\u003Ca href=\"#b3\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b3\"\u003E3\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. AIS is increasingly being used in civil and industrial fields, such as logistics and transportation\u003Csup\u003E[\u003Ca href=\"#b4\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b4\"\u003E4\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, power system inspection, and ocean exploration, as well as military fields\u003Csup\u003E[\u003Ca href=\"#b5\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b5\"\u003E5\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, including demining and blasting, battlefield surveillance, and combat confrontation. Their unique capability to replace humans in complex and high-risk environments renders them invaluable tools. However, as task demands grow in difficulty and complexity, single unmanned systems face limitations in information access and problem-solving capacity. It is necessary for AIS to deal with current difficulties through a distributed approach, which offers advantages such as spatial distribution, parallel task execution, and fault tolerance. AIS has become a new trend in future research due to its comprehensive information acquisition and ability to realize intelligent interaction and processing in response to mission requirements, compared to single-unmanned systems.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EThe AIS must perceive the environment to perform autonomous planning, and the prediction part of planning can be realized by optimizing the future state through the distributed model predictive control (DMPC) method. As an optimal control algorithm based on an optimization problem that can handle constraints efficiently, DMPC is widely used in power systems\u003Csup\u003E[\u003Ca href=\"#b6\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b6\"\u003E6\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, chemical processes\u003Csup\u003E[\u003Ca href=\"#b7\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b7\"\u003E7\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, urban transportation\u003Csup\u003E[\u003Ca href=\"#b8\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b8\"\u003E8\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and manufacturing systems\u003Csup\u003E[\u003Ca href=\"#b9\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b9\"\u003E9\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. As a distributed online rolling computation algorithm, DMPC allows AIS to navigate physical and environmental constraints, making it increasingly popular in AIS applications.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EAs the crucial components of AIS, the cooperative control of unmanned aerial vehicles (UAVs) and vehicle platoon systems has received much attention. UAVs play a vital role in several fields, such as disaster relief, environmental monitoring, logistics, transportation, and military surveillance. Through cooperative control, UAVs can quickly and efficiently cover large areas, perform complex missions, and enhance the response speed and success rates of missions\u003Csup\u003E[\u003Ca href=\"#b10\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b10\"\u003E10\u003C\u002Fa\u003E-\u003Ca href=\"#b12\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b12\"\u003E12\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and vehicle platooning systems achieve efficient fleet management, reduce traffic congestion, and save energy consumption in various scenarios such as freight transportation, autonomous driving, and traffic management in modern urban environments, thus improving transportation efficiency and road safety\u003Csup\u003E[\u003Ca href=\"#b13\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b13\"\u003E13\u003C\u002Fa\u003E-\u003Ca href=\"#b15\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b15\"\u003E15\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The difference between UAVs and vehicle platoon systems is that UAVs operate in a three-dimensional airspace, relying on technologies such as GPS, inertial navigation systems, and radar. In contrast, vehicle platoons operate in a two-dimensional road network, responding to traffic regulations, road conditions, and other vehicles, often using vehicle-to-everything (V2X) communications and light detection and ranging (LiDAR) technologies. UAVs have a more limited range due to battery limitations, while vehicle platoons are more accessible to refuel or recharge and have a longer range. However, UAVs and vehicle platoon systems are similar in several ways, e.g., both involve cooperative control of multiple independent units and require real-time decision-making and communication to achieve common goals; both require real-time control in a dynamic and uncertain environment to ensure efficient operation and safety; both need to consider physical and network security. Despite some differences, UAVs and vehicle platoon systems share commonalities in core technologies such as cooperative control, multi-subsystems communication and path optimization, all of which can be effectively handled under the framework of DMPC. Meanwhile, considering the significance of the cooperative operation between UAVs and vehicle platoon systems in both civil and military fields, an overview of the two systems can help to promote the integration of the two fields, inspire researchers to explore the cooperative operation of these two systems and promote the development of integrated solutions in AIS.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EAlthough existing review articles have covered a wide range of research on DMPC in different application scenarios, such as smart grids\u003Csup\u003E[\u003Ca href=\"#b16\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b16\"\u003E16\u003C\u002Fa\u003E-\u003Ca href=\"#b18\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b18\"\u003E18\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, networked control systems\u003Csup\u003E[\u003Ca href=\"#b19\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b19\"\u003E19\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, autonomous ground vehicles (AGVs)\u003Csup\u003E[\u003Ca href=\"#b20\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b20\"\u003E20\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, each has specific focuses and limitations. For example, Arauz \u003Ci\u003Eet al\u003C\u002Fi\u003E. concentrated on the application of DMPC in network control problems, with special emphasis on its vulnerabilities and defense mechanisms in network security\u003Csup\u003E[\u003Ca href=\"#b19\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b19\"\u003E19\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. On the other hand, Yu \u003Ci\u003Eet al\u003C\u002Fi\u003E. comprehensively reviewed the application of model predictive control (MPC) in single and multiple AGVs\u003Csup\u003E[\u003Ca href=\"#b20\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b20\"\u003E20\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Notably, Negenborn \u003Ci\u003Eet al\u003C\u002Fi\u003E. surveyed and categorized a wide range of DMPC methods, offering insights into the historical development and research trends of these methods\u003Csup\u003E[\u003Ca href=\"#b21\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b21\"\u003E21\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. However, none of these reviews have specifically addressed the application of DMPC to two critical domains - UAVs and vehicle platoon systems nor have they discussed the unique challenges and future research directions for DMPC within these systems.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn contrast to existing reviews, this review systematically introduces the basic fundamentals of DMPC and its theoretical achievements in multi-agent systems (MASs), with a unique focus on the application of DMPC in two AIS subsystems: UAVs and vehicle platoon systems. It also highlights the shortcomings and challenges of the existing methods in practical applications and discusses the direction of future research to promote DMPC in UAVs and vehicle platoon systems. This review presents the basics of DMPC with theoretical foundations in MASs in Section 2. Sections 3 and 4 review the DMPC applications in UAVs and vehicle platoon systems, respectively. Section 5 discusses the existing shortcomings and challenges of the DMPC approach for AIS. Finally, the conclusion is provided in Section 6.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2\" class=\"article-Section\"\u003E\u003Ch2 \u003E2. PRELIMINARY FOR DMPC\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EBefore introducing the application of DMPC in UAVs and vehicle platoon systems, this section will introduce the basics of DMPC and the advances of its theoretical research in MASs.\u003C\u002Fp\u003E\u003Cdiv id=\"s2-1\" class=\"article-Section\"\u003E\u003Ch3 \u003E2.1 MPC\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EMPC is derived from optimal control, which computes for a sequence of control inputs by optimizing a cost function containing information about the system's states and control inputs at a future time and explicitly handling the constraints imposed on the system\u003Csup\u003E[\u003Ca href=\"#b22\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b22\"\u003E22\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. MPC employs a rolling optimization strategy, which optimizes over a finite time horizon. Considering a discrete-time system \u003Cinline-formula\u003E\u003Ctex-math id=\"M1\"\u003E$$ x(t+1)=f(x(t), u(t)) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E as an example, where the system is sampled at a specific sampling instant \u003Cinline-formula\u003E\u003Ctex-math id=\"M2\"\u003E$$ t $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, and the currently sampled state information \u003Cinline-formula\u003E\u003Ctex-math id=\"M3\"\u003E$$ x(t) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is used as the initial state based on the model of the system to predict the state of the system in the prediction horizon \u003Cinline-formula\u003E\u003Ctex-math id=\"M4\"\u003E$$ [t, t+N] $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E. Simultaneously, a constrained open-loop optimization problem is solved for a given system cost function to obtain a set of control input sequences. The first control input in this sequence is then applied to the actual controlled system. The new state of the system is obtained by sampling at the next sampling instant \u003Cinline-formula\u003E\u003Ctex-math id=\"M5\"\u003E$$ t+1 $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, and this process is performed repeatedly. The specific process is shown in \u003Ca href=\"#Figure1\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure1\"\u003EFigure 1\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"Figure-block\" id=\"Figure1\"\u003E\u003Cdiv xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxhtml\" class=\"article-figure-image\"\u003E\u003Ca href=\"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure1\" class=\"Article-img\" alt=\"\" target=\"_blank\"\u003E\u003Cimg alt=\"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" src=\"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-1.jpg\" class=\"\" title=\"\" alt=\"\" \u002F\u003E\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"article-figure-note\"\u003E\u003Cp class=\"figure-note\"\u003E\u003C\u002Fp\u003E\u003Cp class=\"figure-note\"\u003EFigure 1. MPC strategy. MPC: Model predictive control.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"\"\u003EMPC has been widely used in linear systems\u003Csup\u003E[\u003Ca href=\"#b23\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b23\"\u003E23\u003C\u002Fa\u003E,\u003Ca href=\"#b24\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b24\"\u003E24\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and nonlinear systems\u003Csup\u003E[\u003Ca href=\"#b25\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b25\"\u003E25\u003C\u002Fa\u003E,\u003Ca href=\"#b26\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b26\"\u003E26\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, but it is not the focus of this paper. There are quite a few foundations for MPC research, such as robust MPC methods to cope with external disturbances\u003Csup\u003E[\u003Ca href=\"#b27\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b27\"\u003E27\u003C\u002Fa\u003E-\u003Ca href=\"#b29\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b29\"\u003E29\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, tracking MPC methods to achieve the designed control objectives\u003Csup\u003E[\u003Ca href=\"#b30\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b30\"\u003E30\u003C\u002Fa\u003E,\u003Ca href=\"#b31\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b31\"\u003E31\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and economic model predictive control (EMPC) methods considering economic costs in the actual production process\u003Csup\u003E[\u003Ca href=\"#b32\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b32\"\u003E32\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Recently, the data-driven MPC methods were proposed by Berberich \u003Ci\u003Eet al\u003C\u002Fi\u003E., and a rigorous theoretical analysis was given\u003Csup\u003E[\u003Ca href=\"#b31\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b31\"\u003E31\u003C\u002Fa\u003E,\u003Ca href=\"#b33\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b33\"\u003E33\u003C\u002Fa\u003E,\u003Ca href=\"#b34\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b34\"\u003E34\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For more information about the advances in theoretical research on MPC and the application of MPC methods in robotics, UAVs, and other systems, readers can refer to Ref.\u003Csup\u003E[\u003Ca href=\"#b35\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b35\"\u003E35\u003C\u002Fa\u003E-\u003Ca href=\"#b39\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b39\"\u003E39\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-2\" class=\"article-Section\"\u003E\u003Ch3 \u003E2.2 DMPC\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EAs the scale of engineering systems increases, the applicability of traditional MPC methods diminishes. Instead, the DMPC method has received more attention for its excellent capability of dealing with complex large-scale systems characterized by high dimensionality, multiple subsystems, constraints, and targets. Unlike the centralized architecture of traditional MPC methods, DMPC decomposes the global system into several subsystems and formulates a local optimization problem for each subsystem, allowing the complex optimization problem of a large-scale system to be divided into simple subproblems. This approach significantly reduces the scale and computational complexity of individual optimization problems\u003Csup\u003E[\u003Ca href=\"#b40\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b40\"\u003E40\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. A quantitative comparison of some key performances between centralized MPC and DMPC is shown in \u003Ca href=\"#Figure2\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure2\"\u003EFigure 2\u003C\u002Fa\u003E. With the DMPC strategy, information can be exchanged between subsystems, and interaction is also allowed between the local model prediction controllers of each subsystem. The structure of DMPC is schematically illustrated in \u003Ca href=\"#Figure3\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure3\"\u003EFigure 3\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\u003Cdiv class=\"Figure-block\" id=\"Figure2\"\u003E\u003Cdiv xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxhtml\" class=\"article-figure-image\"\u003E\u003Ca href=\"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure2\" class=\"Article-img\" alt=\"\" target=\"_blank\"\u003E\u003Cimg alt=\"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" src=\"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-2.jpg\" class=\"\" title=\"\" alt=\"\" \u002F\u003E\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"article-figure-note\"\u003E\u003Cp class=\"figure-note\"\u003E\u003C\u002Fp\u003E\u003Cp class=\"figure-note\"\u003EFigure 2. Quantitative comparison of key performances between centralized MPC and DMPC. MPC: Model predictive control; DMPC: distributed model predictive control.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"Figure-block\" id=\"Figure3\"\u003E\u003Cdiv xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxhtml\" class=\"article-figure-image\"\u003E\u003Ca href=\"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure3\" class=\"Article-img\" alt=\"\" target=\"_blank\"\u003E\u003Cimg alt=\"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" src=\"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-3.jpg\" class=\"\" title=\"\" alt=\"\" \u002F\u003E\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"article-figure-note\"\u003E\u003Cp class=\"figure-note\"\u003E\u003C\u002Fp\u003E\u003Cp class=\"figure-note\"\u003EFigure 3. DMPC structure. DMPC: Distributed model predictive control.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"\"\u003EIn the following, a commonly used DMPC standard framework will be introduced, including the determination of optimization problem, cost function, and information transmission in DMPC.\u003C\u002Fp\u003E\u003Cdiv id=\"s2-2-1\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.2.1 Optimization problem\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EA general discrete system is taken as an example to introduce the optimization problem of DMPC:\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(1)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E1\"\u003E $$ \\begin{equation} x_i(t+1)=f_i(x_i(t), u_i(t), x_{-i}(t)) \\end{equation} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003Ewhere \u003Cinline-formula\u003E\u003Ctex-math id=\"M6\"\u003E$$ x_i(t) \\in \\mathbb{R}^{n_i} $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, \u003Cinline-formula\u003E\u003Ctex-math id=\"M7\"\u003E$$ u_i(t) \\in \\mathbb{R}^{m_i} $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E denote the state and control input vector of the subsystem \u003Cinline-formula\u003E\u003Ctex-math id=\"M8\"\u003E$$ i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, respectively, and \u003Cinline-formula\u003E\u003Ctex-math id=\"M9\"\u003E$$ x_{-i}(t) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E represents the state of the subsystem that has information interaction with subsystem \u003Cinline-formula\u003E\u003Ctex-math id=\"M10\"\u003E$$ i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E. Furthermore, the system states and the control inputs must satisfy the constraints: \u003Cinline-formula\u003E\u003Ctex-math id=\"M11\"\u003E$$ x_i(t)\\in \\mathbb{X}_i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E and \u003Cinline-formula\u003E\u003Ctex-math id=\"M12\"\u003E$$ u_i(t)\\in \\mathbb{U}_i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, respectively, where \u003Cinline-formula\u003E\u003Ctex-math id=\"M13\"\u003E$$ \\mathbb{X}_i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E and \u003Cinline-formula\u003E\u003Ctex-math id=\"M14\"\u003E$$ \\mathbb{U}_i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E are convex sets containing the origin.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn DMPC, each subsystem optimizes only its local cost function, and its local optimization problem is given as:\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E（2）\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2\"\u003E\r\n \r\n$$\r\n\\min\\limits_{u_i(t+s|t)}J_i(x_i, u_i, x_{-i})\r\n$$\r\n \r\n\u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(2a)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2a\"\u003E $$ \\begin{align*} s.t.\\;\\;&x_i(t+s+1|t)=f_i(x_i(t+s|t), u_i(t+s|t), x_{-i}(t+s|t)) \\end{align*} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(2b)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2b\"\u003E $$ \\begin{align*} &{x}_i(t|t)=x_i(t) \\end{align*} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(2c)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2c\"\u003E $$ \\begin{align*} &x_i(t+s|t) \\in \\mathbb{X}_i \\end{align*} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(2d)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2d\"\u003E $$ \\begin{align*} &u_i(t+s|t) \\in \\mathbb{U}_i \\end{align*} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(2e)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E2e\"\u003E $$ \\begin{align*} &x_i(t+N|t) \\in \\mathbb{X}_f^i \\end{align*} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003Ewhere \u003Cinline-formula\u003E\u003Ctex-math id=\"M15\"\u003E$$ s = 1, ..., N-1 $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, \u003Cinline-formula\u003E\u003Ctex-math id=\"M16\"\u003E$$ J_i(x_i, u_i, x_{-i}) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is the objective cost function of the problem, and \u003Cinline-formula\u003E\u003Ctex-math id=\"M17\"\u003E$$ x_i(t+s|t) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is the state predicted at instant \u003Cinline-formula\u003E\u003Ctex-math id=\"M18\"\u003E$$ t $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E for the instant \u003Cinline-formula\u003E\u003Ctex-math id=\"M19\"\u003E$$ t+s $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E. The terminal term \u003Cinline-formula\u003E\u003Ctex-math id=\"M20\"\u003E$$ x_i(t+N|t) \\in \\mathbb{X}_f^i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is often used to ensure the stability of the system.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-2-2\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.2.2 Cost function\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EThe cost function \u003Cinline-formula\u003E\u003Ctex-math id=\"M21\"\u003E$$ J_i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E defines the control objectives of the system and guides the direction of the optimization process. However, since different tasks have varying requirements, the design of the cost function must be adapted to specific application scenarios. For instance, in UAV formation control, the cost function may prioritize maintaining formation shape and avoiding collisions, whereas in vehicle platooning, it might emphasize speed coordination and fuel efficiency. Therefore, the formulation of the cost function should not only be consistent with the overall objectives of the control system but should also accurately reflect the specific demands of a given task, thereby enabling efficient and cooperative control in a complex system. The following is a common form of DMPC cost function:\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(3)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E3\"\u003E $$ \\begin{equation} J_i= \\sum\\limits_{s=0}^{N-1} l(x_i(t+s|t), u_i(t+s|t))+V_c(x_i(t+s|t), x_{-i}(t+s|t))+V_f(x_i(t+N|t)) \\end{equation} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EHere, \u003Cinline-formula\u003E\u003Ctex-math id=\"M22\"\u003E$$ l(x_i(t+s|t), u_i(t+s|t) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E represents the stage cost at the instant \u003Cinline-formula\u003E\u003Ctex-math id=\"M23\"\u003E$$ t+s $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E, and \u003Cinline-formula\u003E\u003Ctex-math id=\"M24\"\u003E$$ V_c(x_i(t+s|t), x_{-i}(t+s|t)) $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E denotes the coupling cost term that containing the state of both subsystem \u003Cinline-formula\u003E\u003Ctex-math id=\"M25\"\u003E$$ i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E and its neighbors. Additionally, in DMPC, it is often necessary to include a coupling cost that incorporates information about neighboring subsystems in the cost function. The information transmission between the neighbors will be introduced in the following sections.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-2-3\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.2.3 Information transmission\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EIn DMPC, the interaction of information between subsystems and the sequence of solving the optimization problem is critical for achieving efficient cooperative control. Typically, the sequence of optimization problem solving and transmission can be categorized into three approaches: The first is sequential solving and transmission, where each subsystem sequentially solves the problem in a predetermined order and transmits the results to other related subsystems. The advantage of this approach lies in its clear flow and easy-to-implement sequence control, but it may lead to delays in the overall system. The second approach is synchronous solving and transmission, where all the subsystems start solving simultaneously and transmit the information at the same instant, which minimizes the latency but requires high communication and computational resources. The third approach is asynchronous solving and transmission, where each subsystem independently completes the solving and transmission on its own time scale, allowing for a certain degree of non-simultaneity and thus increasing system flexibility. To illustrate the different characteristics of these approaches more intuitively, \u003Ca href=\"#Figure4\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure4\"\u003EFigure 4\u003C\u002Fa\u003E presents the sequences of optimization problem-solving and information transmission in the DMPC strategy for a MAS with three agents as an example.\u003C\u002Fp\u003E\u003Cdiv class=\"Figure-block\" id=\"Figure4\"\u003E\u003Cdiv xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxhtml\" class=\"article-figure-image\"\u003E\u003Ca href=\"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure4\" class=\"Article-img\" alt=\"\" target=\"_blank\"\u003E\u003Cimg alt=\"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" src=\"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-4.jpg\" class=\"\" title=\"\" alt=\"\" \u002F\u003E\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"article-figure-note\"\u003E\u003Cp class=\"figure-note\"\u003E\u003C\u002Fp\u003E\u003Cp class=\"figure-note\"\u003EFigure 4. Information interaction between subsystems and the sequence of solving optimization problems. (A) sequential solving and transmission; (B) synchronous solving and transmission; (C) asynchronous solving and transmission.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"\"\u003EIn DMPC, subsystems usually need predictive state information of their neighbors at the current moment in the length of the prediction horizon \u003Cinline-formula\u003E\u003Ctex-math id=\"M26\"\u003E$$ N $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E to construct the optimization problem. There are generally two main approaches to constructing this predicted state information. The first method is that the neighbor first constructs a complete sequence of predicted states that satisfies the required length of the current subsystem, and then transmits this information to the needed subsystem. The advantage of this approach is that the subsystem can directly utilize the complete information for computation, although it may impose a significant data transmission burden. The second approach is that the neighbor transmits only a part of the necessary state information while the receiver subsystem performs specific calculations based on the received data to construct the necessary neighboring state sequence. This approach can reduce the burden of data transmission, but may require additional computational resources and more complex algorithm design to ensure that the constructed state information can satisfy the requirements of control accuracy. These two methods of information construction enable DMPC to achieve efficient and accurate information interaction and cooperative control in complex systems.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EMoreover, existing DMPC algorithms can be classified based on the topology of the transmission network, the information exchange protocols used among local controllers, and the type of cost function considered in the local optimization problem. Depending on whether or not the performance metrics of other subsystems are included in the local cost function, DMPC algorithms can be categorized into coordinated and uncoordinated approaches. Specifically, if each local controller holds global information and minimizes the global cost function, it is referred to as coordinated DMPC\u003Csup\u003E[\u003Ca href=\"#b41\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b41\"\u003E41\u003C\u002Fa\u003E-\u003Ca href=\"#b43\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b43\"\u003E43\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Conversely, if each local predictive controller possesses local information, considers the information of its neighbors in the network topology, and uses the information of its neighbors as useful information for its local optimization problem and minimizes the local cost function, it is referred to as uncoordinated DMPC\u003Csup\u003E[\u003Ca href=\"#b44\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b44\"\u003E44\u003C\u002Fa\u003E-\u003Ca href=\"#b48\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b48\"\u003E48\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Compared with coordinated DMPC, in uncoordinated DMPC, each local controller only needs to exchange information with its associated subsystems, which have lower network requirements. Since uncoordinated DMPC only improves its performance during the optimization process, the overall performance of the system is weaker than that of the coordination algorithm based on the global cost function, but it has more flexibility for the control of each subsystem. In most uncoordinated DMPC, local controllers generally use parallel computation to solve the optimization problems of each subsystem simultaneously\u003Csup\u003E[\u003Ca href=\"#b46\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b46\"\u003E46\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. When controllers operate asynchronously, a corresponding communication strategy for asynchronous transmission is necessary\u003Csup\u003E[\u003Ca href=\"#b47\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b47\"\u003E47\u003C\u002Fa\u003E,\u003Ca href=\"#b48\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b48\"\u003E48\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In the UAVs and vehicle platoon systems targeted in this paper, most of the studies are based on uncoordinated DMPC.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-2-4\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.2.4 Computational complexity\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003ETo analyze the computational complexity of DMPC, it is first necessary to distinguish between linear and nonlinear systems. In linear systems, the computational complexity of DMPC is relatively low due to the availability of efficient solution methods, such as linear programming (LP) or quadratic programming (QP), which have polynomial-time computational complexity. In contrast, DMPC problems for nonlinear systems necessitate the utilization of nonlinear programming (NLP) methodologies, which are inherently more intricate since the solution process entails a greater number of iterative procedures and possesses a higher computational complexity. Furthermore, as the system state dimension increases and the prediction horizon lengthens, the computational complexity rises. An increase in state dimension results in a larger state space, necessitating greater computational resources for state prediction and optimization at each time step. Additionally, a longer prediction horizon expands the size of the optimization problem, as computations must be performed over a more extended prediction horizon, significantly increasing the computational burden. However, a longer prediction horizon also offers enhanced control performance. Therefore, it is necessary to balance control accuracy and computational complexity to ensure that the system can be optimized and controlled in real-time within a reasonable timeframe.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-2-5\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.2.5 Scalability\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EThe scalability of coordinated and uncoordinated DMPC schemes, as discussed in the previous section, will be analyzed in the following. For coordinated DMPC, each local controller needs to optimize the local cost function and consider the global information. This implies that as the number of subsystems increases, the computational burden of the controller will increase with the global information. In contrast, most uncoordinated DMPC schemes exhibit better scalability. In uncoordinated DMPC, each local controller only optimizes its local cost function, so the increase in the number of subsystems does not directly affect the computational complexity of each controller. However, although the computational burden does not increase, the rise in the number of subsystems may result in each subsystem interacting with more neighboring systems, increasing the frequency of information exchange and the amount of communication. As the system grows in size, more complex communication networks may introduce additional burdens, such as delayed information delivery and data loss. Therefore, in the application of large-scale systems, despite the superior performance of uncoordinated DMPC in terms of computational complexity, it is still necessary to address the challenges posed by increasingly complex communication topologies to ensure the overall performance and reliability of the system.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ESince DMPC methods vary considerably when applied to different physical systems and task requirements, this paper will first briefly review the theoretical results of DMPC to MASs in the following subsection. These results can be utilized in the control of UAVs and vehicle platoon systems, as discussed in this paper.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-3\" class=\"article-Section\"\u003E\u003Ch3 \u003E2.3 DMPC in MASs\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EThis section provides a brief review of the theoretical research on DMPC in MASs, dividing the research problems into three key aspects: the existence of disturbances, limited communication and computing resources, and network unreliability.\u003C\u002Fp\u003E\u003Cdiv id=\"s2-3-1\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.3.1 The existence of disturbances\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EIn MASs, different agents collaborate through communication to achieve the given task objectives. As the system becomes larger and more complex, deviations from the actual system during modeling and identification become inevitable. Simultaneously, the complex system is increasingly influenced by the external environment, and these disturbances can be classified as external disturbances. A key research direction in this context is the development of robust DMPC strategies to counter external disturbances. The min-max MPC method, which generates optimal control sequences for the system under the \"worst-case\" disturbance scenario to ensure robust stability, was first proposed by Campo \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b49\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b49\"\u003E49\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Jia \u003Ci\u003Eet al\u003C\u002Fi\u003E. later extended this method to closed-loop DMPC systems by taking feedback control information into account\u003Csup\u003E[\u003Ca href=\"#b50\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b50\"\u003E50\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wei \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed the min-max DMPC method with a self-triggered scheme for the case of multiple parameter uncertainties and external disturbances to achieve robust control under communication delays\u003Csup\u003E[\u003Ca href=\"#b47\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b47\"\u003E47\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn addition, the robust MPC based on \"tube\" proposed by Mayne is also a classical approach to deal with disturbance\u003Csup\u003E[\u003Ca href=\"#b51\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b51\"\u003E51\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In MASs, for instance, Li \u003Ci\u003Eet al\u003C\u002Fi\u003E. utilized the tube method to satisfy local robust constraints and applied a modified alternating direction method of multipliers (ADMM) to solve the optimization problem\u003Csup\u003E[\u003Ca href=\"#b52\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b52\"\u003E52\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For disturbed leader-follower systems, Li \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a fully inclusive control algorithm based on tube-DMPC to deal with the problem that the follower may break away from the convex packet under disturbance\u003Csup\u003E[\u003Ca href=\"#b53\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b53\"\u003E53\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Based on the DMPC method and the tube-based auxiliary controller, Li \u003Ci\u003Eet al\u003C\u002Fi\u003E. realized the robust control of the MASs\u003Csup\u003E[\u003Ca href=\"#b54\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b54\"\u003E54\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-3-2\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.3.2 Limited communication and computing resources\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EIn the communication process of MASs, communication resources are usually limited due to network bandwidth constraints. Additionally, the computational ability of subsystems in distributed architectures is generally weak, and their computational resources are valuable. While event-triggered control is a better choice in terms of reducing the number of communications and optimization problem solving, for perturbed systems, achieving better control while saving computational resources is a direction of great interest. Zou \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed an event-triggered scheme using the information of neighbors to achieve a balance between resource usage and control performance for MASs subject to bounded disturbance\u003Csup\u003E[\u003Ca href=\"#b48\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b48\"\u003E48\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Yang \u003Ci\u003Eet al\u003C\u002Fi\u003E. also proposed a similar adaptive event-triggered DMPC scheme\u003Csup\u003E[\u003Ca href=\"#b55\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b55\"\u003E55\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, self-triggered DMPC schemes have gradually received attention due to the reduction of the number of samples in the system. Zhan \u003Ci\u003Eet al\u003C\u002Fi\u003E. studied the application of a self-triggered scheme in linear MAS consensus\u003Csup\u003E[\u003Ca href=\"#b56\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b56\"\u003E56\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and Mi \u003Ci\u003Eet al\u003C\u002Fi\u003E. solved the dynamically decoupled MAS collaboration problem\u003Csup\u003E[\u003Ca href=\"#b57\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b57\"\u003E57\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Both Wei \u003Ci\u003Eet al\u003C\u002Fi\u003E. and Wang \u003Ci\u003Eet al\u003C\u002Fi\u003E. applied the self-triggered scheme to nonlinear MASs\u003Csup\u003E[\u003Ca href=\"#b47\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b47\"\u003E47\u003C\u002Fa\u003E,\u003Ca href=\"#b58\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b58\"\u003E58\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Based on the disturbance observer and self-triggered DMPC scheme, Yang \u003Ci\u003Eet al\u003C\u002Fi\u003E. similarly achieved the collaborative control of nonlinear MASs\u003Csup\u003E[\u003Ca href=\"#b59\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b59\"\u003E59\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s2-3-3\" class=\"article-Section\"\u003E\u003Ch4 \u003E2.3.3 Network unreliability\u003C\u002Fh4\u003E\u003Cp class=\"\"\u003EThe agents interact with the physical environment, communicate local information, and update the information of their neighbors, which requires connectivity, reliability, and security of the communication networks. DMPC-based control methods also need to take network security issues into account. Velarde \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a resilient DMPC control strategy that considers insider attacks\u003Csup\u003E[\u003Ca href=\"#b60\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b60\"\u003E60\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Ananduta \u003Ci\u003Eet al\u003C\u002Fi\u003E. introduced an iterative DMPC strategy to mitigate the effects of false data injection attacks\u003Csup\u003E[\u003Ca href=\"#b61\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b61\"\u003E61\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Many studies regard denial of service (DOS) attacks as a data loss problem for MASs. For example, Dai \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a resilient robust DMPC scheme based on an extended sequence transmission strategy to eliminate the adverse effects under DOS attacks\u003Csup\u003E[\u003Ca href=\"#b62\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b62\"\u003E62\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and Chen \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a similar event-triggered DMPC scheme\u003Csup\u003E[\u003Ca href=\"#b63\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b63\"\u003E63\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wei \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a novel scheme for detecting distributed attacks using the DMPC method to achieve consensus of linear MASs under adversarial attacks\u003Csup\u003E[\u003Ca href=\"#b64\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b64\"\u003E64\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ETo address the vulnerability of network communication, Hahn \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a robust DMPC scheme for affine dynamical subsystems under communication delays\u003Csup\u003E[\u003Ca href=\"#b65\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b65\"\u003E65\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Su \u003Ci\u003Eet al\u003C\u002Fi\u003E. addressed the tracking consistency problem by designing a DMPC strategy for linear MASs affected by disturbance and time-varying communication delays\u003Csup\u003E[\u003Ca href=\"#b66\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b66\"\u003E66\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wang \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed an event-triggered DMPC scheme to solve the cooperative control problem for MASs with disturbance, input delays, and communication delays\u003Csup\u003E[\u003Ca href=\"#b67\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b67\"\u003E67\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Franzè \u003Ci\u003Eet al\u003C\u002Fi\u003E. used the concept of reachability analysis to solve the leader-follower formation control problem under the data loss conditions in MASs\u003Csup\u003E[\u003Ca href=\"#b68\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b68\"\u003E68\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Yang \u003Ci\u003Eet al\u003C\u002Fi\u003E. utilized Bernoulli distribution to describe the packet loss phenomenon and selected the prediction horizon of MASs based on an event-triggered scheme to achieve cooperative control\u003Csup\u003E[\u003Ca href=\"#b69\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b69\"\u003E69\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s3\" class=\"article-Section\"\u003E\u003Ch2 \u003E3. DMPC FOR UAVS\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EUAVs have been widely adopted as an emerging technology due to their high flexibility, mobility, and ease of deployment\u003Csup\u003E[\u003Ca href=\"#b10\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b10\"\u003E10\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Given the uncertainty of UAV application scenarios and the complexity of target missions, it is often challenging for an individual UAV to meet evolving mission requirements. UAVs can be controlled in a distributed way, thus realizing that individuals collaborate to perceive the surrounding environment together and complete multiple complex tasks as a whole through information sharing, intelligent collaboration, and autonomous decision-making\u003Csup\u003E[\u003Ca href=\"#b70\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b70\"\u003E70\u003C\u002Fa\u003E,\u003Ca href=\"#b71\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b71\"\u003E71\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Current research demonstrates that, based on the communication links between UAVs, UAVs can rapidly and accurately perform complex tasks such as cooperative path planning, target exploration, and formation control. Additionally, in the military domain, UAVs play a crucial role in essential tasks such as reconnaissance and strikes\u003Csup\u003E[\u003Ca href=\"#b72\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b72\"\u003E72\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For instance, the U.S. Air Force announced the Small UAV System Flight Plan in 2016, strategically confirming the future value of small UAVs and clarifying the concept of UAV swarm operations\u003Csup\u003E[\u003Ca href=\"#b73\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b73\"\u003E73\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, the importance of UAVs continues to grow.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EThe DMPC method has recently received much attention due to its excellent ability to handle constrained optimization problems and fast computational capability. However, the research on the application of DMPC to UAVs still needs to be completed. The following sections provide an overview of the application of DMPC to UAVs in three key areas: trajectory optimization, formation control, and collision avoidance. In addition, \u003Ca href=\"#Table1\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Table1\"\u003ETable 1\u003C\u002Fa\u003E summarizes the existing research on DMPC-based UAVs considering multi-mission scenarios.\u003C\u002Fp\u003E\u003Cdiv id=\"Table1\" class=\"Figure-block\"\u003E\u003Cdiv class=\"table-note\"\u003E\u003Cspan class=\"\"\u003ETable 1\u003C\u002Fspan\u003E\u003Cp class=\"\"\u003EResearch of DMPC-based UAVs considering multi-mission scenarios\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table-responsive article-table\"\u003E\u003Ctable class=\"a-table\"\u003E\u003Cthead\u003E\u003Ctr\u003E\u003Ctd align=\"left\" style=\"class:table_top_border\"\u003E\u003Cb\u003EResearch\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border\"\u003E\u003Cb\u003ETrajectory optimization\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border\"\u003E\u003Cb\u003EFormation control\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border\"\u003E\u003Cb\u003ECollision avoidance\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border\"\u003E\u003Cb\u003ECommunication restrictions\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border\"\u003E\u003Cb\u003EDisturbance and fault\u003C\u002Fb\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Fthead\u003E\u003Ctbody\u003E\u003Ctr\u003E\u003Ctd align=\"left\" style=\"class:table_top_border2\"\u003EBo \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b74\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b74\"\u003E74\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border2\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border2\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border2\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border2\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_top_border2\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EQi \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b75\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b75\"\u003E75\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EYang \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b76\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b76\"\u003E76\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EHu \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b77\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b77\"\u003E77\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EYu \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b78\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b78\"\u003E78\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EGräfe \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b79\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b79\"\u003E79\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003ELi \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b80\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b80\"\u003E80\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EZheng \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b81\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b81\"\u003E81\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EChai \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b82\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b82\"\u003E82\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003ERichards \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b83\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b83\"\u003E83\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EZhang \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b84\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b84\"\u003E84\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EChi \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b85\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b85\"\u003E85\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EZhou \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b86\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b86\"\u003E86\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EChen \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b87\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b87\"\u003E87\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EWen \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b88\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b88\"\u003E88\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003EYuan \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b89\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b89\"\u003E89\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003ELi \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b90\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b90\"\u003E90\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003ENiu \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b91\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b91\"\u003E91\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\"\u003ESun \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b92\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b92\"\u003E92\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003Ctr\u003E\u003Ctd align=\"left\" style=\"class:table_bottom_border\"\u003EJiang \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b93\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b93\"\u003E93\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_bottom_border\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_bottom_border\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_bottom_border\"\u003E√\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_bottom_border\"\u003E\u003C\u002Ftd\u003E\u003Ctd align=\"center\" style=\"class:table_bottom_border\"\u003E\u003C\u002Ftd\u003E\u003C\u002Ftr\u003E\u003C\u002Ftbody\u003E\u003C\u002Ftable\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"table_footer\"\u003E\u003Cdiv class=\"table_footer_note\"\u003E\u003Cp class=\"para\"\u003EDMPC: Distributed model predictive control; UAVs: unmanned aerial vehicles.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s3-1\" class=\"article-Section\"\u003E\u003Ch3 \u003E3.1 Trajectory optimization\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EWhen UAVs operate in coordination, optimizing their generated paths to enhance mission efficiency while reducing overall energy consumption is crucial. The DMPC method can find the optimal paths under environmental constraints based on its ability to minimize the cost function and deal with the constraints, so the use of the DMPC method to provide real-time solutions for UAVs has received more and more attention.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EBo \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered UAV kinematics and collision avoidance constraints to develop a trajectory planning strategy based on DMPC, which achieved better real-time performance and more optimal trajectories compared to traditional trajectory optimization methods\u003Csup\u003E[\u003Ca href=\"#b74\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b74\"\u003E74\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Qi \u003Ci\u003Eet al\u003C\u002Fi\u003E. utilized the DMPC method as a framework to design tracking trajectory optimization for ground targets, and introduced the Nash game method in the optimization solution process, then verified the feasibility of the proposed scheme by simulation\u003Csup\u003E[\u003Ca href=\"#b75\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b75\"\u003E75\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Similarly, Yang \u003Ci\u003Eet al\u003C\u002Fi\u003E. also designed an online trajectory planning strategy based on the DMPC method\u003Csup\u003E[\u003Ca href=\"#b76\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b76\"\u003E76\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and Lun \u003Ci\u003Eet al\u003C\u002Fi\u003E. investigated the application of UAVs as communication relay nodes for maritime vessels, and simulations verified that the designed DMPC algorithm was able to optimize energy costs while achieving UAVs trajectory planning\u003Csup\u003E[\u003Ca href=\"#b94\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b94\"\u003E94\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The optimization problem designed by Ao \u003Ci\u003Eet al\u003C\u002Fi\u003E. combined the A* algorithm with Nash optimization, significantly reducing the solution size of the optimization problem while ensuring high accuracy of the generated trajectories\u003Csup\u003E[\u003Ca href=\"#b95\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b95\"\u003E95\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EMost of the aforementioned DMPC methods focus on basic trajectory optimization, but more complex trajectory planning tasks must account for obstacles, dynamic target tracking, and other challenging scenarios. Hu \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered the movement of the target, obstacles obstructing the line of sight, and energy constraints of the UAVs, and designed a DMPC strategy that balances optimization and prioritization, and experimentally verified the effectiveness of the UAVs in tracking targets in urban environments\u003Csup\u003E[\u003Ca href=\"#b77\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b77\"\u003E77\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Yu \u003Ci\u003Eet al\u003C\u002Fi\u003E. also considered real-time target tracking and combined the adaptive difference algorithm with Nash optimization, and the DMPC was globally optimized with the help of Nash optimization, which improved the accuracy of target tracking\u003Csup\u003E[\u003Ca href=\"#b78\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b78\"\u003E78\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Gräfe \u003Ci\u003Eet al\u003C\u002Fi\u003E. reduced the computational complexity and network traffic required for the DMPC method based on an event-triggered scheme while ensuring the safety and reliability of the generated trajectories\u003Csup\u003E[\u003Ca href=\"#b79\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b79\"\u003E79\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Yin \u003Ci\u003Eet al\u003C\u002Fi\u003E. used a DMPC method to generate trajectories to achieve a stable network connection between the UAVs and the ground control stations\u003Csup\u003E[\u003Ca href=\"#b96\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b96\"\u003E96\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Notably, Luis \u003Ci\u003Eet al\u003C\u002Fi\u003E. utilized online DMPC to generate trajectories of small UAV swarms in real-time and efficiently compute non-collision trajectories in mission scenarios through an on-demand collision avoidance method. The proposed method was shown to reduce flight time by approximately 50% on average in UAV point-to-point transition missions compared to the buffered voronoi cells (BVC)-based collision avoidance method. Meanwhile, the activation function was designed to detect any interference to the UAV, and an event-triggered replanning-based strategy was also devised. The algorithms involved were finally applied to a range of solid UAVs, from 2 to 20, and simulations were conducted to verify the effectiveness of the algorithms under a variety of scenarios, including obstacle-free transitions and transition tasks with static obstacles\u003Csup\u003E[\u003Ca href=\"#b97\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b97\"\u003E97\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Another key research on DMPC is the aerial robot swarms designed by Soria \u003Ci\u003Eet al\u003C\u002Fi\u003E., whose objective functions included separation, propulsion, direction, and control. The quadrotor adjusted its flight trajectory based on interactive information, and the practical experiments with five quadrotors successfully demonstrated the safe flight of multiple drones in complex environments\u003Csup\u003E[\u003Ca href=\"#b98\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b98\"\u003E98\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EThe search task, as a critical operation often performed by UAVs, is closely related to trajectory optimization. It is essential to ensure that the generated trajectories can effectively cover search areas while reducing energy consumption to meet various mission requirements in real-time. The DMPC-based search trajectory generation has been studied in some literature. Du \u003Ci\u003Eet al\u003C\u002Fi\u003E. and Yao \u003Ci\u003Eet al\u003C\u002Fi\u003E. developed UAV search trajectory optimization strategies by combining graph theory\u003Csup\u003E[\u003Ca href=\"#b99\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b99\"\u003E99\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and target probabilistic graph\u003Csup\u003E[\u003Ca href=\"#b100\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b100\"\u003E100\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E under the DMPC framework, respectively. Trajectory optimization becomes particularly challenging in complex environments with unknown obstacles and communication interference. Hence, Li \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed an adaptive guidance DMPC method to reduce exploration loss and improve exploration efficiency\u003Csup\u003E[\u003Ca href=\"#b80\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b80\"\u003E80\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Chai \u003Ci\u003Eet al\u003C\u002Fi\u003E. used Voronoi diagrams to replan the search trajectory in real-time, avoiding the collision between repeated search and UAVs, and still achieved better performance in communication-constrained environments\u003Csup\u003E[\u003Ca href=\"#b82\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b82\"\u003E82\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. It is worth mentioning that Zheng \u003Ci\u003Eet al\u003C\u002Fi\u003E. applied DMPC to UAV collaborative area search by taking the neighbor prediction path as a parameter and distributing the overall search objective function in the constraints between UAVs\u003Csup\u003E[\u003Ca href=\"#b81\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b81\"\u003E81\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Simulation results demonstrated that their algorithm effectively improves search efficiency and verifies the scalability as the number of UAVs increased from 8 to 20.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s3-2\" class=\"article-Section\"\u003E\u003Ch3 \u003E3.2 Formation control\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EThe importance of UAV formation control lies in its ability to enhance mission efficiency and execute tasks such as search, surveillance, and rescue through coordinated formation. Maintaining formation also ensures safe distances between UAVs, safeguarding their operational safety. Research on UAV formation control using the DMPC method began with Richards \u003Ci\u003Eet al\u003C\u002Fi\u003E. in 2004, who proposed a robust DMPC scheme for cooperative UAVs that avoided collisions by satisfying robust constraints. This strategy was significantly less computationally expensive than centralized algorithms and achieved superior tracking control performance\u003Csup\u003E[\u003Ca href=\"#b83\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b83\"\u003E83\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Subsequently, Ru \u003Ci\u003Eet al\u003C\u002Fi\u003E. achieved formation reconfiguration control based on UAVs with different missions, using multi-objective game theory combined with the DMPC method to realize autonomous formation reconfiguration\u003Csup\u003E[\u003Ca href=\"#b101\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b101\"\u003E101\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Based on the DMPC framework, Bian \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed an algorithm for fast formation control of UAVs on circular trajectories, effectively improving the convergence ability of the formation with lower computational consumption\u003Csup\u003E[\u003Ca href=\"#b102\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b102\"\u003E102\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn addition, formation flight in complex situations is widely concerned; considering the different tasks of heterogeneous UAV formation and collision avoidance in formation movement, Zhang \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a DMPC scheme based on adaptive differential evolution\u003Csup\u003E[\u003Ca href=\"#b84\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b84\"\u003E84\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E; Zhao \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed cost functions for leader, coordinator and follower UAVs, respectively, in heterogeneous UAVs, and simulations verified the feasibility of the designed DMPC strategies under the tasks of formation and retention, and insertion of new UAVs into the formation\u003Csup\u003E[\u003Ca href=\"#b103\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b103\"\u003E103\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Chi \u003Ci\u003Eet al\u003C\u002Fi\u003E. achieved safe UAV formations using the particle swarm optimization (PSO) algorithm combined with the DMPC method\u003Csup\u003E[\u003Ca href=\"#b85\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b85\"\u003E85\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, while Liu \u003Ci\u003Eet al\u003C\u002Fi\u003E. realized rapid formation and maintenance of UAVs based on the DMPC method, demonstrating both stability and feasibility\u003Csup\u003E[\u003Ca href=\"#b104\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b104\"\u003E104\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For military applications, formation reconfiguration plays an essential role in performing military missions, such as attacking enemy military targets and searching for targets; Zhou \u003Ci\u003Eet al\u003C\u002Fi\u003E. used the DMPC method while considering communication constraints to achieve UAVs that break through defenses under stealthy conditions\u003Csup\u003E[\u003Ca href=\"#b86\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b86\"\u003E86\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Another related and intriguing issue is collaborative payload transportation. For instance, Wehbeh \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a system model connecting quadcopters with payloads and compared centralized MPC and DMPC schemes\u003Csup\u003E[\u003Ca href=\"#b105\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b105\"\u003E105\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Simulation experiments proved the effectiveness of the designed algorithm.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ERecently, as DMPC has been more widely utilized in UAV formation control, existing studies have begun to consider the constraints of objective factors previously neglected in the literature, such as the limitations of the communication network, external disturbance, and errors due to model inaccuracies. Considering the actual situations of communication failure, Chen \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a formation control algorithm based on relative position information about the relative distances and angles between UAVs, and then realized formation control based on the DMPC method in the presence of communication disturbances and information inaccuracies\u003Csup\u003E[\u003Ca href=\"#b87\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b87\"\u003E87\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wen \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a two-layer MPC scheme for UAVs, where the outer layer used a DMPC strategy to generate optimal control vectors, which combined with the inner layer's tube-based MPC, reduced control errors in UAV formation subjected to disturbance\u003Csup\u003E[\u003Ca href=\"#b88\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b88\"\u003E88\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Yuan \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a DMPC-based data transmission structure to accelerate the convergence of a six-degree-of-freedom UAV formation, with simulations employing data transmission delays following a Gaussian distribution\u003Csup\u003E[\u003Ca href=\"#b89\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b89\"\u003E89\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The designed unidirectional structure was shown to play a crucial role in system convergence, demonstrating the applicability of the proposed DMPC algorithm.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EEncirclement is a tactic used to restrict a target by changing the formation of a group of UAVs. Its purpose is to maintain surveillance and prevent enemy targets from escaping or to protect friendly targets\u003Csup\u003E[\u003Ca href=\"#b106\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b106\"\u003E106\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and the process of encirclement can be viewed as a process of formation change and maintenance. Marasco \u003Ci\u003Eet al\u003C\u002Fi\u003E. developed a strategy to encircle both moving and static targets using a circular formation based on the DMPC method\u003Csup\u003E[\u003Ca href=\"#b107\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b107\"\u003E107\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Based on the designed DMPC algorithm, Hafez \u003Ci\u003Eet al\u003C\u002Fi\u003E. first considered the task allocation strategy in the UAVs in the simulation by estimating the trajectory cost of the target and minimizing the task time. The encirclement effect demonstrated the effectiveness of two UAV teams in encircling stationary and moving targets\u003Csup\u003E[\u003Ca href=\"#b108\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b108\"\u003E108\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s3-3\" class=\"article-Section\"\u003E\u003Ch3 \u003E3.3 Collision avoidance\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EWhen UAVs perform trajectory optimization and formation control, constructing a safe flight trajectory is fundamental to achieving cooperative control. Effective collision avoidance strategies can ensure that UAVs do not collide with obstacles and other aircraft, thus ensuring the integrity of the equipment, reducing the probability of accidents, and improving mission efficiency\u003Csup\u003E[\u003Ca href=\"#b109\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b109\"\u003E109\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn previous research, such as that by Richards \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b83\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b83\"\u003E83\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, Bo \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b74\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b74\"\u003E74\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and Zhang \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b84\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b84\"\u003E84\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, when optimizing trajectories and maintaining UAV formations based on the DMPC method, the safety of the formation was ensured by imposing safety or collision avoidance constraints. In addition, Li \u003Ci\u003Eet al\u003C\u002Fi\u003E. addressed the collision problem at a low cost by designing a collision management unit and designing cooperative collision avoidance rules based on angle changes\u003Csup\u003E[\u003Ca href=\"#b90\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b90\"\u003E90\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. It is worth mentioning that D'Amato \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed an MPC-based collision avoidance system and incorporated the right-of-way rules from the International Civil Aviation Organization (ICAO) to make UAV behavior predictable and compatible with human decision-making. The prediction unit was designed to predict potential collisions and calculate the required constraints, and the simulation results verify the effectiveness and scalability of their scheme\u003Csup\u003E[\u003Ca href=\"#b110\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b110\"\u003E110\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ENiu \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed UAVs to predict the motion trajectories of their neighbors to avoid collisions in situations where communication was impossible, demonstrating the effectiveness of the proposed scheme in scenarios involving no communication and multiple obstacles\u003Csup\u003E[\u003Ca href=\"#b91\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b91\"\u003E91\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, Sun \u003Ci\u003Eet al\u003C\u002Fi\u003E. also adopted a similar approach and employed the improved Quatre algorithm to enhance the stability of UAV formation\u003Csup\u003E[\u003Ca href=\"#b92\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b92\"\u003E92\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Jiang \u003Ci\u003Eet al\u003C\u002Fi\u003E. developed a terminal condition to satisfy the collision avoidance algorithm for DMPC-based UAV formation control, aiming to reduce the conservatism of collision-free safe trajectories\u003Csup\u003E[\u003Ca href=\"#b93\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b93\"\u003E93\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s4\" class=\"article-Section\"\u003E\u003Ch2 \u003E4. DMPC FOR VEHICLE PLATOONS\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EGround vehicles are common tools of transportation and play a significant role in people's lives. With the rapid development of sensors, control systems, and computer technology, expectations for vehicle performance have risen. Research on ground vehicles has focused on AGV platoons due to their potential to reduce traffic congestion, improve traffic efficiency, enhance vehicle safety, and save energy\u003Csup\u003E[\u003Ca href=\"#b20\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b20\"\u003E20\u003C\u002Fa\u003E,\u003Ca href=\"#b111\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b111\"\u003E111\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The effectiveness of vehicle platoons in maintaining safety and saving fuel has been experimentally demonstrated by the PATH program in California\u003Csup\u003E[\u003Ca href=\"#b112\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b112\"\u003E112\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, the Energy ITS program in Japan\u003Csup\u003E[\u003Ca href=\"#b113\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b113\"\u003E113\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and the GCDC program in the Netherlands \u003Csup\u003E[\u003Ca href=\"#b114\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b114\"\u003E114\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EThe primary objective of a vehicle platoon is to synchronize the movement of a group of vehicles by assigning a control role to each vehicle and exchanging information between vehicles to ensure that appropriate safety distances are maintained between adjacent vehicles\u003Csup\u003E[\u003Ca href=\"#b111\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b111\"\u003E111\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. However, this method has limitations that make it challenging to maintain a stable platoon. The advancement of communication technology enables vehicles in a platoon to communicate through wireless or self-organizing networks. This facilitates the design of effective collaborative control strategies, improving the stability and efficiency of the platoon while ensuring smooth cooperative control and operation. \u003Ca href=\"#Figure5\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure5\"\u003EFigure 5\u003C\u002Fa\u003E shows four typical communication methods used in vehicle platoons of a front vehicle \u003Cinline-formula\u003E\u003Ctex-math id=\"M27\"\u003E$$ 0 $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E and \u003Cinline-formula\u003E\u003Ctex-math id=\"M28\"\u003E$$ N $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E rear vehicles\u003Csup\u003E[\u003Ca href=\"#b115\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b115\"\u003E115\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, all of these communication topologies shown in \u003Ca href=\"#Figure5\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"Figure5\"\u003EFigure 5\u003C\u002Fa\u003E can be converted to unidirectional communication.\u003C\u002Fp\u003E\u003Cdiv class=\"Figure-block\" id=\"Figure5\"\u003E\u003Cdiv xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxhtml\" class=\"article-figure-image\"\u003E\u003Ca href=\"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure5\" class=\"Article-img\" alt=\"\" target=\"_blank\"\u003E\u003Cimg alt=\"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" src=\"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-5.jpg\" class=\"\" title=\"\" alt=\"\" \u002F\u003E\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"article-figure-note\"\u003E\u003Cp class=\"figure-note\"\u003E\u003C\u002Fp\u003E\u003Cp class=\"figure-note\"\u003EFigure 5. The directed communication topologies used in vehicle platoon. (A) PF topology; (B) PLF topology; (C) TPF topology; (D) TPLF topology. PF: Predecessor-following; PLF: predecessor-leader following; TPF: two-predecessor following; TPLF: two-predecessor-leader following.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"\"\u003EConsidering a vehicle platoon with a leader, the objective of the platooning is for each following vehicle \u003Cinline-formula\u003E\u003Ctex-math id=\"M29\"\u003E$$ i $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E to maintain an appropriate distance from the follower vehicles and the leader vehicle while following the leader at a speed of \u003Cinline-formula\u003E\u003Ctex-math id=\"M30\"\u003E$$ v_0 $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E. This objective can be given mathematically as:\u003C\u002Fp\u003E\u003Cp class=\"\"\u003E\u003Cdiv class=\"disp-formula\"\u003E\u003Clabel\u003E(4)\u003C\u002Flabel\u003E\u003Ctex-math id=\"E4\"\u003E $$ \\begin{align} \\left\\{ \\begin{array}{ll} \\lim_{t \\rightarrow \\infty}||v_i(t)-v_0(t)||=0\\\\ \\lim_{t \\rightarrow \\infty}||s_{i-1}(t)-s_i(t)-d_{i-1, i}||=0\\\\ \\lim_{t \\rightarrow \\infty}||s_i(t)-s_0(t)-d_0||=0\\\\ \\end{array} \\right. \\end{align} $$ \u003C\u002Ftex-math\u003E\u003C\u002Fdiv\u003E\u003C\u002Fp\u003E\u003Cp class=\"\"\u003Ewhere \u003Cinline-formula\u003E\u003Ctex-math id=\"M31\"\u003E$$ d_{i-1, i} $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is the desired distance between neighboring vehicles, and \u003Cinline-formula\u003E\u003Ctex-math id=\"M32\"\u003E$$ d_0 $$\u003C\u002Ftex-math\u003E\u003C\u002Finline-formula\u003E is the desired distance between a follower vehicle and the leader vehicle. To control vehicle platoon using the DMPC scheme, local information interaction at each vehicle node is required. This approach achieves collaborative motion globally while adhering to the constraints outlined in Equation (4).\u003C\u002Fp\u003E\u003Cdiv id=\"s4-1\" class=\"article-Section\"\u003E\u003Ch3 \u003E4.1 Strategy for platooning\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EIn the DMPC scheme, distributed controllers are deployed in each vehicle to collaborate in solving the constrained optimal control problem (COCP) for platooning over a finite time horizon and to exchange information via vehicle-to-vehicle communication links.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EMaxim \u003Ci\u003Eet al\u003C\u002Fi\u003E. set the constant speed of the leader and established the control strategy for the remaining vehicles; each vehicle was controlled by the DMPC method\u003Csup\u003E[\u003Ca href=\"#b116\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b116\"\u003E116\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Lu \u003Ci\u003Eet al\u003C\u002Fi\u003E. demonstrated the stability of vehicle platoon under unidirectional communication topology for heterogeneous vehicles by designing a cost function based on the difference between the states of a vehicle and its neighboring vehicles\u003Csup\u003E[\u003Ca href=\"#b117\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b117\"\u003E117\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Similarly, Ma \u003Ci\u003Eet al\u003C\u002Fi\u003E. achieved stable control of heterogeneous vehicles using an output feedback-based DMPC strategy\u003Csup\u003E[\u003Ca href=\"#b118\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b118\"\u003E118\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Zheng \u003Ci\u003Eet al\u003C\u002Fi\u003E. presented the trajectory error-based cost functions for heterogeneous vehicles with dynamic coupling; this design ensured stability through equality-based terminal constraints subject to spatial geometric constraints\u003Csup\u003E[\u003Ca href=\"#b115\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b115\"\u003E115\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E; similar studies have appeared in the research of Qiang \u003Ci\u003Eet al\u003C\u002Fi\u003E., they designed a two-layer control architecture, using vehicles with odd numbers as the first layer, sending information to vehicles with even numbers, and ensuring the distance and same speed of vehicles through sequential calculation\u003Csup\u003E[\u003Ca href=\"#b119\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b119\"\u003E119\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, Yu \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered using the Nash optimal DMPC algorithm for platooning, which employed the Nash optimal algorithm to solve the decentralized problem and achieve Nash equilibrium for all vehicles\u003Csup\u003E[\u003Ca href=\"#b120\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b120\"\u003E120\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. To keep the required control rate at the same level as the communication rate, Liu \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a non-iterative DMPC scheme for vehicle platooning, which ensured the stability of the closed-loop system through the linear matrix inequality technique and had compatibility constraints between the neighboring vehicles\u003Csup\u003E[\u003Ca href=\"#b121\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b121\"\u003E121\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The simulation verified the effective control of the vehicle platooning in the presence of joining and leaving vehicles.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ESimilar to the factors to be considered by DMPC in UAVs, computational resources and computational speed determine the ability of the vehicle platoon to deal with emergencies quickly. To solve the problem of shortage of computational resources, Bai \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a parallel DMPC method based on the ADMM, which used the Lagrange multiplier method and the dual decomposition technique\u003Csup\u003E[\u003Ca href=\"#b122\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b122\"\u003E122\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For a mixed fleet of autonomous vehicles and human-driven vehicles, Zhan \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed the ADMM-based DMPC method to obtain the global optimal solution of the local controller for the sub-platoons, which significantly reduced the computational consumption\u003Csup\u003E[\u003Ca href=\"#b123\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b123\"\u003E123\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ETo operate vehicle platoons on real roads, it is essential to account for the fact that the speed of the leader vehicle is time-varying to adapt to the road conditions. To address this problem, Maxim \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a DMPC method for tracking the leader vehicle\u003Csup\u003E[\u003Ca href=\"#b124\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b124\"\u003E124\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. On the other hand, Yan \u003Ci\u003Eet al\u003C\u002Fi\u003E. analyzed the stability and feasibility of the DMPC method for vehicle platooning systems\u003Csup\u003E[\u003Ca href=\"#b125\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b125\"\u003E125\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Qiang \u003Ci\u003Eet al\u003C\u002Fi\u003E. addressed the problem of coupled state vehicles with distance constraints and cost functions, which computed the state-coupled set for decoupling constraints and solved the DMPC optimization problem when the information of the leader vehicle is unknown\u003Csup\u003E[\u003Ca href=\"#b126\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b126\"\u003E126\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Simulation results demonstrated that the proposed algorithm can ensure stable tracking between vehicles even when the lead vehicle has variable inputs.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s4-2\" class=\"article-Section\"\u003E\u003Ch3 \u003E4.2 Robustness of platooning\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EMost research on DMPC-based vehicle platoon control assumes an accurate model. However, model uncertainty, sensor noise, and environmental disturbances can adversely affect the accuracy of the DMPC scheme. Additionally, communication delays and data transmission losses during vehicle-to-vehicle information exchange can further degrade platooning performance. Therefore, robust DMPC schemes should be developed to maintain system stability under these uncertainties.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ELuo \u003Ci\u003Eet al\u003C\u002Fi\u003E. addressed the problem of disturbances and modeling errors in vehicle platoon systems, employing the proportional multiple integral (PMI) observer techniques with unknown inputs to limit the deviation between the actual systems and nominal systems\u003Csup\u003E[\u003Ca href=\"#b127\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b127\"\u003E127\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For the same situation, Ju \u003Ci\u003Eet al\u003C\u002Fi\u003E. also proposed a stochastic DMPC scheme and verified the effectiveness of the control scheme in the presence of model uncertainties\u003Csup\u003E[\u003Ca href=\"#b128\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b128\"\u003E128\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E; Yin \u003Ci\u003Eet al\u003C\u002Fi\u003E. combined Taguchi's robustness with stochastic DMPC scheme to reduce the negative impact of uncertainty on the performance of platooning\u003Csup\u003E[\u003Ca href=\"#b129\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b129\"\u003E129\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. For the vehicle platoon systems subjected only to additive disturbances, Luo \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a robust DMPC scheme for tracking virtual time-varying trajectories for non-complete vehicle platoon systems\u003Csup\u003E[\u003Ca href=\"#b130\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b130\"\u003E130\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and Chen \u003Ci\u003Eet al\u003C\u002Fi\u003E. utilized local and neighbor uncertainty distribution information to collaboratively handle coupled probabilistic constraints in vehicle platoon systems. Based on the designed self-triggered mechanism, a constraint tightening strategy was implemented in the optimization problem to ensure the stability of the systems at the triggering moment. Simulation experiments were also conducted in a vehicle platoon system with five vehicles to verify the effectiveness of the algorithm in the case of queue control and emergency braking\u003Csup\u003E[\u003Ca href=\"#b131\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b131\"\u003E131\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, Mousavi \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered uncertain resources in dynamic environments, incorporating the evolution of vehicles and the environment into the planning strategy, resulting in a general framework consisting of estimation, prediction, and planning\u003Csup\u003E[\u003Ca href=\"#b132\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b132\"\u003E132\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn recent years, research has increasingly focused on data-driven approaches to effectively address inaccuracies in modeling heterogeneous vehicle platoon systems. The basic principle of data-driven modeling is to use the input and output data of the system to construct the system model, and data-driven DMPC methods have been recently investigated by Huang \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b133\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b133\"\u003E133\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, Zheng \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b134\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b134\"\u003E134\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and Kohler \u003Ci\u003Eet al\u003C\u002Fi\u003E\u003Csup\u003E[\u003Ca href=\"#b135\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b135\"\u003E135\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The basic principle of data-driven modeling is to use the input and output data of the system to construct the system model, and data-driven DMPC methods have been recently investigated by Zheng \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b134\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b134\"\u003E134\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and Kohler \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b135\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b135\"\u003E135\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Based on this method, Huang \u003Ci\u003Eet al\u003C\u002Fi\u003E. added a variable for estimating the global consensus distributed across each agent in the optimization problem and actively compensated for the communication delay based on input-output data. The simulation results demonstrated the convergence of the auxiliary variables with the system output, verifying the effectiveness of the designed algorithm under communication delay\u003Csup\u003E[\u003Ca href=\"#b133\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b133\"\u003E133\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wu \u003Ci\u003Eet al\u003C\u002Fi\u003E. established a data-driven model using subspace identification for a heterogeneous vehicle platoon to achieve stability under the DMPC method\u003Csup\u003E[\u003Ca href=\"#b136\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b136\"\u003E136\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. It is worth mentioning that Zhan \u003Ci\u003Eet al\u003C\u002Fi\u003E. mapped the nonlinear model to a high-dimensional linear space based on the theory of the Koopman operator, and designed a neural network framework based on extended dynamic mode decomposition (EDMD) to approximate the Koopman operator. The simulation experiment used 25 vehicles, and the centralized MPC and DMPC methods were used, respectively. The results showed that DMPC can reduce the computational cost. The method has a faster convergence speed than the traditional nonlinear DMPC method\u003Csup\u003E[\u003Ca href=\"#b137\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b137\"\u003E137\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EWhen data losses occur during the communication of vehicle platoons, such as packet losses and communication delays, it is crucial for vehicle platoon control to estimate the lost data and accurately continue the mission. Wang \u003Ci\u003Eet al\u003C\u002Fi\u003E. addressed data estimation under packet loss by designing a DMPC scheme that solves invariant sets and feedback control laws\u003Csup\u003E[\u003Ca href=\"#b67\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b67\"\u003E67\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Pauca \u003Ci\u003Eet al\u003C\u002Fi\u003E. used the information received by the vehicle at the previous moment to alleviate packet losses caused by wireless communication networks that exchanged information between vehicles\u003Csup\u003E[\u003Ca href=\"#b138\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b138\"\u003E138\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In scenarios where inter-vehicle communication is limited and communication delays exist, Xu \u003Ci\u003Eet al\u003C\u002Fi\u003E. used buffers and delay compensators to reduce the interference caused by non-ideal communication\u003Csup\u003E[\u003Ca href=\"#b139\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b139\"\u003E139\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Wang \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed an event-triggered scheme based on state errors and input delays and proposed a compensation scheme for input and communication delays\u003Csup\u003E[\u003Ca href=\"#b67\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b67\"\u003E67\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Similarly, Maxim \u003Ci\u003Eet al\u003C\u002Fi\u003E. and Yan \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed DMPC schemes to achieve stable control of vehicle platoons in the presence of time-varying communication delays\u003Csup\u003E[\u003Ca href=\"#b124\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b124\"\u003E124\u003C\u002Fa\u003E,\u003Ca href=\"#b125\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b125\"\u003E125\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s4-3\" class=\"article-Section\"\u003E\u003Ch3 \u003E4.3 Security of platooning\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EWhen a vehicle platoon is traveling on a roadway, preventing collisions is paramount to ensuring passenger safety, and recent research has focused on enhancing the safety of vehicle platoons. Mohseni \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered the non-holonomic property of the vehicle platoons while predicting the behavior of other vehicles, and designed a cooperative DMPC scheme with predictive collision avoidance features to ensure collision avoidance even when the vehicle deviates from the desired trajectory\u003Csup\u003E[\u003Ca href=\"#b140\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b140\"\u003E140\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Liu \u003Ci\u003Eet al\u003C\u002Fi\u003E. considered the interactions between vehicles and their neighbors, and by analyzing the data of expressway naturalistic driving, the authors summarized the characteristics from aggressive driving behaviors to cautious driving behaviors, and designed collaborative strategies for different driving behaviors. Notably, the proposed DMPC scheme was validated through hardware-in-the-loop simulation, demonstrating its ability to safely perform tasks such as following a vehicle and changing lanes in high-risk situations\u003Csup\u003E[\u003Ca href=\"#b141\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b141\"\u003E141\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, the safe merging problem of heterogeneous vehicle platoons is studied by Liu \u003Ci\u003Eet al\u003C\u002Fi\u003E.\u003Csup\u003E[\u003Ca href=\"#b141\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b141\"\u003E141\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. By designing the collision safety constraints, Gratzer \u003Ci\u003Eet al\u003C\u002Fi\u003E. ensured the stability of the vehicle platoon during sudden braking maneuvers\u003Csup\u003E[\u003Ca href=\"#b142\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b142\"\u003E142\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In the research of Franzè \u003Ci\u003Eet al\u003C\u002Fi\u003E., vehicle platoons could flexibly adjust their topologies in the presence of obstacles, thus ensuring the safe operation of the systems\u003Csup\u003E[\u003Ca href=\"#b143\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b143\"\u003E143\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EEnsuring network security is also crucial for vehicle platoons, as vehicle-to-vehicle information transmission is vulnerable to malicious intrusions and cyber-attacks, which can threaten the stability of the platoon and potentially lead to human injury and property loss. Chen \u003Ci\u003Eet al\u003C\u002Fi\u003E. established a dynamic event triggering scheme with DoS attack sensing capability, where the event triggering threshold was adjusted according to the DoS attack duration and vehicle states. The evolution of vehicle positions, spacing, and speeds in the formation under different event-triggering parameters and DoS attack durations were verified through simulation, demonstrating the resilience and reliability of the designed DMPC algorithm in addressing security challenges\u003Csup\u003E[\u003Ca href=\"#b144\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b144\"\u003E144\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Lyu \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a communication topology safety response system that incorporates the DMPC method and demonstrates that it can effectively ensure the stability and security of the vehicle platoons under cyber-attacks\u003Csup\u003E[\u003Ca href=\"#b145\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b145\"\u003E145\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Zeng \u003Ci\u003Eet al\u003C\u002Fi\u003E. developed a resilient DMPC framework for vehicle platoons under Byzantine attacks, which detected unreliable information based on the resilient set and previously transmitted information, and achieved excellent performance with guaranteed safety\u003Csup\u003E[\u003Ca href=\"#b146\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b146\"\u003E146\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s5\" class=\"article-Section\"\u003E\u003Ch2 \u003E5. CHALLENGES AND FUTURE\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EThe previous sections reviewed the application of DMPC methods in UAVs and vehicle platoon systems, but significant theoretical and implementation challenges remain. This section summarizes the challenges and future of DMPC methods in practical application.\u003C\u002Fp\u003E\u003Cdiv id=\"s5-1\" class=\"article-Section\"\u003E\u003Ch3 \u003E5.1 Security control\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EThe DMPC method has shown great potential in UAVs and vehicle platoon systems, but its safety issues cannot be ignored. Due to the dependence of DMPC on network physical systems, there is a risk of nonmalicious failures, such as communication delays and data loss, which may lead to system instability. In addition, the distributed nature of DMPC makes it vulnerable to network attacks, especially deception attacks\u003Csup\u003E[\u003Ca href=\"#b147\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b147\"\u003E147\u003C\u002Fa\u003E,\u003Ca href=\"#b148\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b148\"\u003E148\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and interrupt attacks\u003Csup\u003E[\u003Ca href=\"#b149\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b149\"\u003E149\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Attackers can tamper with control signals or disrupt communication networks, seriously affecting system performance and potentially causing recursive feasibility and stability issues.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ETo address these security challenges, researchers have proposed various network security control methods and fault tolerant control (FTC) technologies. These approaches are designed to maintain system stability by detecting, identifying, and mitigating the effects of network attacks. For example, a design based on robust DMPC can improve the security margin of the system in the face of network attacks, ensuring the integrity of input signals\u003Csup\u003E[\u003Ca href=\"#b144\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b144\"\u003E144\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, the FTC method mitigates security issues caused by malicious agents by actively isolating faulty subsystems\u003Csup\u003E[\u003Ca href=\"#b150\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b150\"\u003E150\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In Section 4.3 of the previous text, a brief statement was made regarding the network communication security control issues of vehicle platoon systems. However, the security control issues of UAVs and vehicle platoon systems based on DMPC still require further research. In recent years, emerging technologies such as cloud computing and blockchain have also demonstrated the potential to enhance the security of DMPC\u003Csup\u003E[\u003Ca href=\"#b151\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b151\"\u003E151\u003C\u002Fa\u003E,\u003Ca href=\"#b152\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b152\"\u003E152\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. The cloud-based MPC framework can utilize encryption technology to keep data encrypted during transmission and processing, thereby preventing data leakage and attacks\u003Csup\u003E[\u003Ca href=\"#b153\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b153\"\u003E153\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Meanwhile, blockchain technology has the potential to provide a secure distributed information exchange platform for MASs, thereby further enhancing the ability of the system to resist attacks\u003Csup\u003E[\u003Ca href=\"#b154\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b154\"\u003E154\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In the future, the development of DMPC methods will rely on the combination of stronger network defense mechanisms and FTC methods. The incorporation of cutting-edge technologies such as cloud computing and blockchain will be critical in developing more secure and resilient distributed control systems, particularly for applications with stringent security requirements, such as UAVs and vehicle platoon systems.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s5-2\" class=\"article-Section\"\u003E\u003Ch3 \u003E5.2 Data-driven control\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EMost of the existing DMPC methods are based on accurate system models, but considering the difficulty in obtaining models in actual systems or the use of imprecise and unstable models, there are significant differences between theoretical and actual results. Data-driven control, by contrast, is a method that does not depend on an exact system model. It generates control inputs through a designed algorithm based on data obtained by the system over a period of historical time, which can solve the current problem of DMPC relying on an exact model. Kohler \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a linear data-driven DMPC scheme with dynamic coupling features based on Willems' Fundamental Lemma \u003Csup\u003E[\u003Ca href=\"#b135\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b135\"\u003E135\u003C\u002Fa\u003E,\u003Ca href=\"#b155\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b155\"\u003E155\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Additionally, researchers have proposed scalable data-driven DMPC schemes\u003Csup\u003E[\u003Ca href=\"#b156\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b156\"\u003E156\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E for large-scale systems, dissipative behavior-based data-driven DMPC schemes\u003Csup\u003E[\u003Ca href=\"#b157\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b157\"\u003E157\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and data-driven DMPC schemes for direct current (DC) microgrids\u003Csup\u003E[\u003Ca href=\"#b158\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b158\"\u003E158\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and complex traffic network management\u003Csup\u003E[\u003Ca href=\"#b159\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b159\"\u003E159\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In addition, Fawcett \u003Ci\u003Eet al\u003C\u002Fi\u003E. successfully achieved robust motion control of quadruped robots in complex environments by combining behavioral system theory with distributed data-driven predictive control technology\u003Csup\u003E[\u003Ca href=\"#b160\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b160\"\u003E160\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, which demonstrated the effectiveness of data-driven methods in different systems. As noted earlier, the application of data-driven DMPC in vehicle exhaust systems to handle solutions with uncertain dynamics has gained significant attention\u003Csup\u003E[\u003Ca href=\"#b136\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b136\"\u003E136\u003C\u002Fa\u003E,\u003Ca href=\"#b137\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b137\"\u003E137\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In summary, data-driven DMPC has shown outstanding performance in handling dynamic responses and optimizing control of unknown complex systems, demonstrating its extensive potential and development prospects in multiple fields. However, in current data-driven DMPC research, how to ensure that robust data-driven DMPC methods can be obtained even if the data is unreliable or partially missing still needs to be studied.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EIn addition to traditional data-driven DMPC control schemes, there is growing interest in data-driven DMPC approaches based on learning methods. Gros \u003Ci\u003Eet al\u003C\u002Fi\u003E. demonstrated that reinforcement learning (RL) could achieve stable MPC control under model uncertainty and also studied the presence of disturbances\u003Csup\u003E[\u003Ca href=\"#b161\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b161\"\u003E161\u003C\u002Fa\u003E,\u003Ca href=\"#b162\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b162\"\u003E162\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Mallick \u003Ci\u003Eet al\u003C\u002Fi\u003E. extended this work to MASs, implementing RL and deployment of DMPC as a function approximator\u003Csup\u003E[\u003Ca href=\"#b163\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b163\"\u003E163\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Similarly, Liu \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed a neural network-based DMPC approximator that successfully reduced the computational burden of DMPC in large-scale systems\u003Csup\u003E[\u003Ca href=\"#b164\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b164\"\u003E164\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Another learning-based approach utilizes deep learning, such as combining long short-term memory (LSTM) units with MPC schemes to reduce energy consumption\u003Csup\u003E[\u003Ca href=\"#b165\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b165\"\u003E165\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, using deep belief networks to find the optimal control list for MPC for sewage treatment \u003Csup\u003E[\u003Ca href=\"#b166\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b166\"\u003E166\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, and combining autoencoders with MPC for automatic power generation control\u003Csup\u003E[\u003Ca href=\"#b167\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b167\"\u003E167\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Notably, Salzmann \u003Ci\u003Eet al\u003C\u002Fi\u003E. implemented real-time onboard tracking control for quadcopters using deep learning and MPC\u003Csup\u003E[\u003Ca href=\"#b168\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b168\"\u003E168\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. However, there have been limited achievements in combining DMPC schemes with deep learning. Yin \u003Ci\u003Eet al\u003C\u002Fi\u003E. combined LSTM units with convolutional neural networks (CNN) for feature extraction and prediction of offshore wind farms, and then used DMPC for control\u003Csup\u003E[\u003Ca href=\"#b169\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b169\"\u003E169\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. D'Alfonso \u003Ci\u003Eet al\u003C\u002Fi\u003E. used deep RL combined with DMPC to achieve vehicle exhaust control\u003Csup\u003E[\u003Ca href=\"#b170\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b170\"\u003E170\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Given the powerful ability of deep learning to capture system features, especially in complex nonlinear and large-scale systems, its combination with DMPC can significantly enhance the dynamic modeling capability of the system. In the future, it is essential to focus on the computational efficiency and dynamic adaptability of data-driven DMPC solutions to enable their application in a broader range of scenarios, such as UAVs and vehicle platoon systems.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s5-3\" class=\"article-Section\"\u003E\u003Ch3 \u003E5.3 Practical limitations\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EIn addition to considering the theoretical challenges of DMPC, it is also crucial to address the practical challenges that arise during the implementation of DMPC in UAVs and vehicle exhaust systems. A primary challenge is hardware limitations, as actual system models are often nonlinear, requiring nonlinear model predictive control (NMPC) methods instead of linear MPC calculations in most cases. Compared to the most advanced non-predictive methods, NMPC imposes significantly higher computational demands, making it difficult to deal with the nonlinear optimization problems on vehicles and UAVs with limited processing power\u003Csup\u003E[\u003Ca href=\"#b171\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b171\"\u003E171\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. This issue is more prominent in UAVs with more limited memory and computing resources. Additionally, some hardware components may impose further constraints on the construction of MPC problems, thereby affecting the feasibility of these problems. Some constraints require the design of DMPC strategies with higher computational efficiency and lower power consumption. With further development of hardware and nonlinear optimization solvers\u003Csup\u003E[\u003Ca href=\"#b172\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b172\"\u003E172\u003C\u002Fa\u003E,\u003Ca href=\"#b173\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b173\"\u003E173\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, as well as computational research based on field programmable gate arrays (FPGA)\u003Csup\u003E[\u003Ca href=\"#b174\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b174\"\u003E174\u003C\u002Fa\u003E,\u003Ca href=\"#b175\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b175\"\u003E175\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E and microprocessors\u003Csup\u003E[\u003Ca href=\"#b176\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b176\"\u003E176\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, running NMPC algorithm with nonlinear fully dynamic models on embedded computers has become easier to compute. However, obtaining more efficient solutions to reduce hardware limitations remains an open problem.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ECommunication delay presents another critical challenge. In distributed control systems, particularly in UAVs and vehicle platoon systems, effective communication is essential for coordination. Sections 2.4 and 4.2 in the previous text have discussed some situations where communication delays and packet loss occur in UAVs and vehicle platoon systems. Due to factors such as signal attenuation, channel congestion, and external radio interference, data transmission may be delayed or lost, which can degrade the performance of DMPC, leading to suboptimal control actions or even system instability, thereby jeopardizing the safety of the systems. Therefore, it is crucial to incorporate robust communication protocols and consider delay compensation techniques within the DMPC framework, and there have been numerous theoretical studies that have taken into account communication delays or packet loss situations\u003Csup\u003E[\u003Ca href=\"#b66\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b66\"\u003E66\u003C\u002Fa\u003E,\u003Ca href=\"#b67\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b67\"\u003E67\u003C\u002Fa\u003E,\u003Ca href=\"#b177\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b177\"\u003E177\u003C\u002Fa\u003E,\u003Ca href=\"#b178\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b178\"\u003E178\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. However, in practical implementation, due to the limitations of hardware to some extent, few studies have verified the practical effectiveness of theoretical DMPC schemes through hardware-in-the-loop simulations\u003Csup\u003E[\u003Ca href=\"#b179\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b179\"\u003E179\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. This issue merits further consideration in future research.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EEnvironmental factors also play an essential role in the practical deployment of DMPC. Uncertain dynamic environments, such as constantly changing weather conditions, obstacles in forests or complex terrains, sudden road accidents, and occasional pedestrians in UAVs and vehicle platoon systems, present significant challenges to the safety and robustness of DMPC strategies. The DMPC strategy must be adaptable and resilient to possible uncertain situations to ensure safe and reliable operation in real-world scenarios. For MPC-based approaches, Lindqvist \u003Ci\u003Eet al\u003C\u002Fi\u003E. proposed a method for UAVs to quickly handle dynamic obstacles. However, there are still limitations in relying on motion capture systems to detect obstacles clearly\u003Csup\u003E[\u003Ca href=\"#b180\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b180\"\u003E180\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Batkovic \u003Ci\u003Eet al\u003C\u002Fi\u003E. designed the auto drive system for cycling based on the model predictive flexible trajectory tracking control (MPFTC) framework to deal with unforeseen road emergencies\u003Csup\u003E[\u003Ca href=\"#b181\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b181\"\u003E181\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. In a distributed scenario, obstacle avoidance trajectory planning in complex environments for UAVs has been proposed \u003Csup\u003E[\u003Ca href=\"#b98\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b98\"\u003E98\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Additionally, scenario-based MPC methods have emerged as a potential solution to the challenges posed by changing environments\u003Csup\u003E[\u003Ca href=\"#b182\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b182\"\u003E182\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, which can introduce factors such as terrain into the prediction range and adjust the control strategy in advance to maintain the system performance in changeable environment\u003Csup\u003E[\u003Ca href=\"#b183\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b183\"\u003E183\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E. Furthermore, methods based on machine learning\u003Csup\u003E[\u003Ca href=\"#b168\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b168\"\u003E168\u003C\u002Fa\u003E,\u003Ca href=\"#b184\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b184\"\u003E184\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E or RL\u003Csup\u003E[\u003Ca href=\"#b161\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b161\"\u003E161\u003C\u002Fa\u003E,\u003Ca href=\"#b185\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b185\"\u003E185\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E can make the system robust to dynamic environments through online learning and adaptive strategies, and also have the potential to be applied to participate in designing DMPC strategies in dynamic environments.\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EThe design of DMPC performance parameters, such as the state weight matrix and control weight matrix, plays a crucial role in determining the effectiveness and efficiency of control strategies. These parameters significantly influence the behavior of the system, affecting its stability, robustness, and convergence speed. However, traditional methods for designing these parameters often rely on human expertise and intuition, introducing a degree of randomness and subjectivity into the algorithm implementation process. Although RL-based parameter update methods have demonstrated the ability to achieve desired control effects even with imprecise parameters\u003Csup\u003E[\u003Ca href=\"#b161\" class=\"Link_style\" data-jats-ref-type=\"bibr\" data-jats-rid=\"b161\"\u003E161\u003C\u002Fa\u003E]\u003C\u002Fsup\u003E, designing an adaptive parameter adjustment scheme suitable for different systems or using learning-based methods such as RL and neural networks to find better parameters and apply them well to practical systems is still worth further research.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s6\" class=\"article-Section\"\u003E\u003Ch2 \u003E6. CONCLUSIONS\u003C\u002Fh2\u003E\u003Cp class=\"\"\u003EThis paper reviews the application of DMPC methods in UAVs and vehicle platoon systems. These systems rely on communication to exchange information and coordinate tasks such as trajectory planning, formation control, and platoon control through DMPC methods. Additionally, considering the robustness and security of AIS, DMPC methods must address complex environmental constraints, external disturbances, and cyber-attacks. While there is a foundation of research on these issues, further investigation is needed to address more practical and complex mission scenarios. This paper also summarizes the challenges faced by existing DMPC methods in AIS. However, the work presented here has its limitations. The application examples provided in this paper aim to help readers understand current research directions and challenges, and to inform future work.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7\" class=\"article-Section\"\u003E\u003Ch2 \u003EDECLARATIONS\u003C\u002Fh2\u003E\u003Cdiv id=\"s7-1\" class=\"article-Section\"\u003E\u003Ch3 \u003EAuthors' contributions\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EProject administration: Yan H\u003C\u002Fp\u003E\u003Cp class=\"\"\u003EWriting original draft: Peng Y\u003C\u002Fp\u003E\u003Cp class=\"\"\u003ECommentary and critical review: Rao K, Yang P, Lv Y\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-2\" class=\"article-Section\"\u003E\u003Ch3 \u003EAvailability of data and materials\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003ENot applicable.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-3\" class=\"article-Section\"\u003E\u003Ch3 \u003EFinancial support and sponsorship\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EThis work is supported by the National Natural Science Foundation of China (62333005) and the Innovation Program of Shanghai Municipal Education Commission (2021-01-07-00-02-E00105).\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-4\" class=\"article-Section\"\u003E\u003Ch3 \u003EConflicts of interest\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003EYan H is an Editorial Board Member of the journal \u003Ci\u003EIntelligence & Robotics\u003C\u002Fi\u003E and the guest editor of the Special Issue \"Robot System Intelligentization and Application: Learning, Control and Decision\", while the other authors have declared that they have no conflicts of interest.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-5\" class=\"article-Section\"\u003E\u003Ch3 \u003EEthical approval and consent to participate\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003ENot applicable.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-6\" class=\"article-Section\"\u003E\u003Ch3 \u003EConsent for publication\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003ENot applicable.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003Cdiv id=\"s7-7\" class=\"article-Section\"\u003E\u003Ch3 \u003ECopyright\u003C\u002Fh3\u003E\u003Cp class=\"\"\u003E© The Author(s) 2024.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E",translate:[{language:N,new_title:B,new_abstract:C,new_keywords:aB,is_check:e},{language:"cn",new_title:"无人机和车队系统的分布式模型预测控制：评述",new_abstract:"本文审查了分布式模型预测控制（DMPC）在具有无人机（UAVs）和车队系统的自主智能系统（AIS）中的应用。DMPC是一种最优控制方法，通过预测未来状态并基于系统模型来解决优化问题以调整控制策略，同时管理约束条件，这种技术已被应用到越来越多的工业领域。无人机和车队系统作为AIS的重要组成部分，在民用、工业和军事领域受到广泛关注。DMPC能够实时快速解决优化问题，并考虑到系统未来状态的预测，这与AIS在做出决策时能够预测环境的能力很好地契合，因此在AIS中应用DMPC具有自然优势。本文首先介绍了DMPC的基本原理和在多智体系统（MASs）中的理论结果，然后审查了将DMPC方法应用于无人机和车队系统的情况。最后，总结了现有方法面临的挑战，以提供对未来DMPC在实际应用中的发展的见解。",new_keywords:"分布式模型预测控制，自治智能系统，多Agent系统，无人机，车队系统",is_check:c},{language:"de",new_title:"Verteiltes modellprädiktives Regelungssystem für unbemannte Luftfahrzeuge und Fahrzeugkolonnen: Eine Übersicht",new_abstract:"Dieses Papier untersucht die Anwendung von verteiltem modellprädiktivem Regelung (DMPC) für autonome intelligente Systeme (AIS) mit unbemannten Luftfahrzeugen (UAVs) und Fahrzeugkolonnen-Systemen. DMPC ist eine optimale Regelungsmethode, die Optimierungsprobleme formuliert und löst, um Steuerungsstrategien anzupassen, indem zukünftige Zustände basierend auf Systemmodellen vorhergesagt werden, während gleichzeitig Einschränkungen verwaltet werden. Diese Technik wurde auf eine wachsende Anzahl von industriellen Bereichen angewendet. Als wesentliche Bestandteile von AIS haben UAVs und Fahrzeugkolonnen-Systeme in den zivilen, industriellen und militärischen Bereichen umfangreiche Aufmerksamkeit erhalten. DMPC hat die Fähigkeit, Optimierungsprobleme in Echtzeit schnell zu lösen, während die Vorhersage des zukünftigen Zustands des Systems berücksichtigt wird, was gut zur Fähigkeit von AIS passt, die Umgebung bei Entscheidungen vorherzusagen. Daher hat die Anwendung von DMPC in AIS einen natürlichen Vorteil. Dieses Papier stellt zunächst die Grundprinzipien von DMPC und die theoretischen Ergebnisse in Multi-Agenten-Systemen (MAS) vor. Es untersucht dann die Anwendung von DMPC-Methoden auf UAVs und Fahrzeugkolonnen-Systeme. Schließlich werden die Herausforderungen der bestehenden Methoden zusammengefasst, um Einblicke in die zukünftige Entwicklung von DMPC in praktischen Anwendungen zu bieten.",new_keywords:"Verteilte modellprädiktive Regelung, autonome intelligente Systeme, Multi-Agenten-Systeme, unbemannte Luftfahrzeuge, Fahrzeugkolonnen-Systeme.",is_check:c},{language:"fa",new_title:"Contrôle prédictif distribué pour les véhicules aériens sans pilote et les systèmes de convoi de véhicules : une revue",new_abstract:"Cet article passe en revue l'application du contrôle prédictif distribué (DMPC) pour les systèmes intelligents autonomes (AIS) avec des véhicules aériens sans pilote (UAV) et des systèmes de convoi de véhicules. Le DMPC est une méthode de contrôle optimal qui formule et résout des problèmes d'optimisation pour ajuster les stratégies de contrôle en prévoyant les états futurs basés sur les modèles du système tout en gérant les contraintes, et cette technique a été appliquée dans un nombre croissant de domaines industriels. En tant que composantes essentielles des AIS, les UAV et les systèmes de convoi de véhicules ont reçu une attention considérable dans les domaines civil, industriel et militaire. Le DMPC a la capacité de résoudre rapidement des problèmes d'optimisation en temps réel tout en prenant en compte la prédiction de l'état futur du système, ce qui s'adapte bien à la capacité des AIS de prédire l'environnement lors de la prise de décisions, de sorte que l'application du DMPC dans les AIS présente un avantage naturel. Cet article présente d'abord les principes de base du DMPC et les résultats théoriques dans les systèmes multi-agent (MAS). Il passe ensuite en revue l'application des méthodes DMPC aux UAV et aux systèmes de convoi de véhicules. Enfin, les défis des méthodes existantes sont résumés pour offrir des perspectives sur l'avancement du développement futur du DMPC dans les applications pratiques.",new_keywords:"Contrôle prédictif distribué, systèmes autonomes intelligents, systèmes multi-agents, véhicules aériens sans pilote, systèmes de convoi de véhicules.",is_check:c},{language:"jp",new_title:"無人航空機と車両プラトーンシステムのための分散型予測制御：レビュー",new_abstract:"この論文は、自律的なインテリジェントシステム（AIS）における分散型モデル予測制御（DMPC）の適用について、無人航空機（UAV）および車両プラトーンシステムに焦点を当てて検討しています。DMPCは、最適制御手法であり、システムモデルに基づいて将来の状態を予測し、制約を管理しながら制御戦略を調整するための最適化問題を設定および解決します。この技術は、ますます多くの産業領域に適用されています。AISの重要な部分であるUAVや車両プラトーンシステムは、市民、産業、軍事分野で広範な注目を集めています。DMPCは、システムの将来の状態を予測しながらリアルタイムで最適化問題を迅速に解決する能力を持っており、AISが意思決定を行う際に環境を予測する能力と良くマッチしているため、DMPCのAISへの適用は自然な利点を持っています。この論文では、まずDMPCの基本原則と多エージェントシステム（MAS）における理論的結果を紹介します。その後、DMPC手法のUAVおよび車両プラトーンシステムへの適用について検討します。最後に、既存の手法の課題をまとめ、実用的な応用におけるDMPCの将来の発展を促進するための示唆を提供します。",new_keywords:"分散型モデル予測制御、自律型知能システム、マルチエージェントシステム、無人航空機、車両プラトンシステム",is_check:c},{language:"py",new_title:"Распределенное модельное прогнозирование управления для беспилотных воздушных судов и систем патрулирования транспортных средств: обзор",new_abstract:"Этот документ рассматривает применение распределенного модельного предиктивного управления (DMPC) для автономных интеллектуальных систем (AIS) с беспилотными воздушными судами (UAV) и системами автомобильных плутонов. DMPC - это оптимальный метод управления, который формулирует и решает задачи оптимизации для корректировки стратегий управления путем прогнозирования будущего состояния на основе моделей системы при управлении ограничениями, и эта техника была применена во все более широком спектре промышленности. Как существенные части AIS, беспилотные воздушные суда и системы автомобильных плутонов получили обширное внимание в гражданской, промышленной и военной областях. DMPC имеет способность быстро решать задачи оптимизации в реальном времени, учитывая прогнозирование будущего состояния системы, что хорошо сочетается с способностью AIS предсказывать окружающую среду при принятии решений, поэтому применение DMPC в AIS имеет естественное преимущество. Этот документ сначала представляет основные принципы DMPC и теоретические результаты в мультиагентных системах (MAS). Затем он рассматривает применение методов DMPC к беспилотным воздушным судам и системам автомобильных плутонов. Наконец, кратко описываются вызовы существующих методов, чтобы предложить идеи для продвижения будущего развития DMPC в практических приложениях.",new_keywords:"Распределенное прогнозное управление, автономные интеллектуальные системы, многопользовательские системы, беспилотные воздушные суда, системы платаунов транспортных средств",is_check:c},{language:"sk",new_title:"무인 항공기 및 차량 플라툰 시스템을 위한 분산 모델 예측 제어: 서론",new_abstract:"이 논문은 분산 모델 예측 제어(DMPC)의 적용을 살펴봅니다. 이는 무인 항공기(UAVs) 및 차량 펠튼 시스템과 같은 자율 지능 시스템(AIS)에 대한 것입니다. DMPC는 시스템 모델을 기반으로 미래 상태를 예측하고 제어 전략을 조정하기 위한 최적 제어 방법으로, 제약 조건을 관리하면서 최적화 문제를 공식화하고 해결합니다. 이 기술은 산업 분야에서 점점 더 많이 적용되고 있습니다. AIS의 중요한 부분인 UAVs 및 차량 펠튼 시스템은 민간, 산업 및 군사 분야에서 광범위한 주목을 받았습니다. DMPC는 시스템의 미래 상태 예측을 고려하면서 실시간으로 최적화 문제를 빠르게 해결할 수 있는 능력을 가지고 있어서 AIS의 환경 예측 결정 능력과 자연스럽게 어울립니다. 본 논문은 먼저 DMPC의 기본 원리와 다중 에이전트 시스템(MASs)의 이론적 결과를 소개합니다. 그런 다음 DMPC 방법을 UAVs 및 차량 펠튼 시스템에 적용한 사례를 검토합니다. 마지막으로, 기존 방법의 도전 과제를 요약하여 DMPC의 미래 발전을 촉진하기 위한 통찰을 제공합니다.",new_keywords:"분산 모델 예측 제어, 자율 지능형 시스템, 다중 에이전트 시스템, 무인 항공기, 차량 편대 시스템",is_check:c},{language:"it",new_title:"Controllo predittivo distribuito per veicoli aerei senza pilota e sistemi di piatto veicolare: una panoramica",new_abstract:"Questo articolo esamina l'applicazione del controllo predittivo distribuito (DMPC) per i sistemi intelligenti autonomi (AIS) con veicoli aerei senza pilota (UAV) e sistemi di convoy di veicoli. Il DMPC è un metodo di controllo ottimale che formula e risolve problemi di ottimizzazione per regolare le strategie di controllo prevedendo gli stati futuri basati sui modelli di sistema mentre gestisce vincoli, e questa tecnica è stata applicata in un numero crescente di settori industriali. Come parti essenziali degli AIS, i UAV e i sistemi di convoy di veicoli hanno ricevuto un'ampia attenzione nei settori civili, industriali e militari. Il DMPC ha la capacità di risolvere rapidamente i problemi di ottimizzazione in tempo reale tenendo conto della previsione dello stato futuro del sistema, che si adatta bene alla capacità degli AIS di prevedere l'ambiente durante la presa di decisioni, quindi l'applicazione del DMPC negli AIS ha un vantaggio naturale. Questo articolo introduce innanzitutto i principi di base del DMPC e i risultati teorici nei sistemi multi-agente (MASs). Successivamente, esamina l'applicazione dei metodi DMPC agli UAV e ai sistemi di convoy di veicoli. Infine, vengono riassunte le sfide dei metodi esistenti per offrire spunti per promuovere lo sviluppo futuro del DMPC nelle applicazioni pratiche.",new_keywords:"Controllo predittivo distribuito, sistemi intelligenti autonomi, sistemi multi-agente, veicoli aerei senza equipaggio, sistemi di convoglio di veicoli.",is_check:c},{language:"fs",new_title:"Control predictivo distribuido para vehículos aéreos no tripulados y sistemas de convoy de vehículos: una revisión",new_abstract:"Este documento revisa la aplicación del control predictivo distribuido (DMPC) para sistemas inteligentes autónomos (AIS) con vehículos aéreos no tripulados (UAV) y sistemas de convoy de vehículos. DMPC es un método de control óptimo que formula y resuelve problemas de optimización para ajustar estrategias de control al predecir estados futuros basados en modelos del sistema mientras administra restricciones, y esta técnica se ha aplicado a un número creciente de áreas industriales. Como partes esenciales de AIS, los UAV y los sistemas de convoy de vehículos han recibido una extensa atención en los campos civil, industrial y militar. DMPC tiene la capacidad de resolver rápidamente problemas de optimización en tiempo real teniendo en cuenta la predicción del estado futuro del sistema, lo cual se adapta bien a la capacidad de AIS para predecir el entorno al tomar decisiones, por lo que la aplicación de DMPC en AIS tiene una ventaja natural. Este documento primero introduce los principios básicos de DMPC y los resultados teóricos en sistemas multiagente (MAS). Luego revisa la aplicación de métodos DMPC en UAV y sistemas de convoy de vehículos. Finalmente, se resumen los desafíos de los métodos existentes para ofrecer ideas para avanzar en el desarrollo futuro de DMPC en aplicaciones prácticas.",new_keywords:"Control predictivo distribuido, sistemas inteligentes autónomos, sistemas de múltiples agentes, vehículos aéreos no tripulados, sistemas de convoy de vehículos.",is_check:c},{language:"po",new_title:"Controle preditivo distribuído para veículos aéreos não tripulados e sistemas de comboios de veículos: uma revisão.",new_abstract:"Este artigo revisa a aplicação do controle preditivo distribuído (DMPC) para sistemas inteligentes autônomos (AIS) com veículos aéreos não tripulados (UAVs) e sistemas de comboio de veículos. O DMPC é um método de controle ótimo que formula e resolve problemas de otimização para ajustar as estratégias de controle prevendo estados futuros com base em modelos do sistema, ao mesmo tempo que gerencia as restrições, e essa técnica tem sido aplicada a um número crescente de áreas industriais. Como partes essenciais do AIS, os UAVs e os sistemas de comboio de veículos têm recebido atenção extensa nos campos civil, industrial e militar. O DMPC tem a capacidade de resolver rapidamente problemas de otimização em tempo real levando em conta a previsão do estado futuro do sistema, o que se encaixa bem com a capacidade do AIS de prever o ambiente ao tomar decisões, então a aplicação do DMPC no AIS tem uma vantagem natural. Este artigo primeiro introduz os princípios básicos do DMPC e os resultados teóricos em sistemas multiagente (MASs). Em seguida, revisa a aplicação de métodos de DMPC em UAVs e sistemas de comboio de veículos. Por fim, os desafios dos métodos existentes são resumidos para oferecer insights para avançar no desenvolvimento futuro do DMPC em aplicações práticas.",new_keywords:"Controle preditivo distribuído, sistemas inteligentes autônomos, sistemas de múltiplos agentes, veículos aéreos não tripulados, sistemas de comboios de veículos.",is_check:c}]},ArtDataF:[{id:2256439,article_id:b,reference_num:c,reference:"Aceto G, Persico V, Pescapé A. A Survey on information and communication technologies for industry 4.0: state-of-the-art, taxonomies, perspectives, and challenges. \u003Ci\u003EIEEE Commun Surv Tutorials\u003C\u002Fi\u003E 2019;21:3467-501.",refdoi:"https:\u002F\u002Fdx.doi.org\u002F10.1109\u002FCOMST.2019.2938259",pubmed:a,pmc:a},{id:2256440,article_id:b,reference_num:e,reference:"Griffiths F, Ooi M. 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IEEE; 2023. pp. 507–14.",refdoi:"https:\u002F\u002Fdx.doi.org\u002F10.1109\u002FICUAS57906.2023.10156232",pubmed:a,pmc:a}],ArtDataP:[{href:"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure1",post_id:"Figure1",image:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-1.jpg"},{href:"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure2",post_id:"Figure2",image:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-2.jpg"},{href:"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure3",post_id:"Figure3",image:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-3.jpg"},{href:"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure4",post_id:"Figure4",image:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-4.jpg"},{href:"\u002Farticles\u002Fir.2024.19\u002Fimage\u002FFigure5",post_id:"Figure5",image:"https:\u002F\u002Fimage.oaes.cc\u002Fe7dd7fcd-3c45-4298-b9e2-ec23a759ec19\u002Fir4019-5.jpg"}],ArtDataT:[{date_published:1710691200,section:p,section_id:i,title:F,doi:"10.20517\u002Fir.2024.06",abstract:"\u003Cp\u003EThis paper focuses on the high-level specification and generation of 3D models for operational environments using the idea of \u003Ci\u003Eactive queries\u003C\u002Fi\u003E as a basis for specifying and generating multi-agent plans for acquiring such models. Assuming an underlying multi-agent system, an operator can specify a request for a particular type of model from a specific region by specifying an active query. This declarative query is then interpreted and executed by collecting already existing data\u002Finformation in agent systems or, in the active case, by automatically generating high-level mission plans for agents to retrieve and generate parts of the model that do not already exist. The purpose of an active query is to hide the complexity of multi-agent mission plan generation, data transformations, and distributed collection of data\u002Finformation in underlying multi-agent systems. A description of an active query system, its integration with an existing multi-agent system and validation of the active query system in field robotics experimentation using Unmanned Aerial Vehicles and simulations are provided.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F116da797-64a4-4b6b-9b14-5e8aa07d4bc3\u002Fir4006.pdf",elocation_id:f,fpage:aE,article_id:E,viewed:d,downloaded:d,video_url:"https:\u002F\u002Fv.oaes.cc\u002Fuploads\u002F20240322\u002Fcc456175dd7947988212be95ed46373a.mp4",volume:T,year:D,tag:"87-106",image:q,authors:aF,video_img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20240322\u002Fd29f64531e1c413686ecc81ba4390457.jpg",journal_path:m,lpage:106,author:aF,specialissue:{id:1243,name:" Scene Understanding for Autonomous Robotics"},specialinfo:a,url_doi:G},{date_published:1690214400,section:p,section_id:i,title:I,doi:"10.20517\u002Fir.2023.19",abstract:"\u003Cp\u003EThis paper investigates the robust distributed model predictive control (DMPC) of connected vehicle platoon (CVP) systems subject to denial-of-service (DoS) attacks. The main objective is to design a DMPC algorithm that enables the CVP system to achieve exponential tracking performance. First, a switched system model is proposed for the networked CVP system in the presence of DoS attacks. Then the sufficient conditions for the exponential stability of tracking the performance of the CVP control system under DoS attacks are obtained by constructing a specific Lyapunov function and using the topological matrix decoupling technique. In our paper, the DoS attack phenomenon is handled by introducing the frequency and duration parameters, and a quantitative relationship between the exponential decay rate of the CVP system and the DoS attacks parameters is established based on the conditions proposed in the system design, and the critical value of the DoS attack duration ratio is also derived. Finally, the effectiveness of the proposed algorithm is verified through a simulation of a CVP system consisting of one leading vehicle and three following vehicles.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F3fcdf3fa-781b-4274-b2ff-a6340d6654e6\u002Fir3019.pdf",elocation_id:f,fpage:288,article_id:H,viewed:151,downloaded:10,video_url:f,volume:U,year:2023,tag:"288-305",image:"https:\u002F\u002Foaepublishstorage.blob.core.windows.net\u002F3fcdf3fa-781b-4274-b2ff-a6340d6654e6\u002Fir3019-coverimg.jpg",authors:aG,video_img:a,journal_path:m,lpage:305,author:aG,specialissue:{id:V,name:W},specialinfo:a,url_doi:J,image_list:"https:\u002F\u002Fimage.oaes.cc\u002F3fcdf3fa-781b-4274-b2ff-a6340d6654e6\u002Fir3019-coverimg.jpg"},{date_published:1660924800,section:p,section_id:i,title:L,doi:"10.20517\u002Fir.2022.19",abstract:"\u003Cp\u003EThis paper focuses on the leader-following consensus problem of discrete-time multi-agent systems subject to channel fading under switching topologies. First, a topology switching-based channel fading model is established to describe the information fading of the communication channel among agents, which also considers the channel fading from leader to follower and from follower to follower. It is more general than models in the existing literature that only consider follower-to-follower fading. For discrete multi-agent systems, the existing literature usually adopts time series or Markov process to characterize topology switching while ignoring the more general semi-Markov process. Based on the advantages and properties of semi-Markov processes, discrete semi-Markov jump processes are adopted to model network topology switching. Then, the semi-Markov kernel approach for handling discrete semi-Markov jumping systems is exploited and some novel sufficient conditions to ensure the leader-following mean square consensus of closed-loop systems are derived. Furthermore, the distributed consensus protocol is proposed by means of the stochastic Lyapunov stability theory so that the underlying systems can achieve ℋ\u003Csub\u003E∞\u003C\u002Fsub\u003E consensus performance index. In addition, the proposed method is extended to the scenario where the semi-Markov kernel of semi-Markov switching topologies is not completely accessible. Finally, a simulation example is given to verify the results proposed in this paper. Compared with the existing literature, the method in this paper is more effective and general.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F44befa84-3a12-4bd5-90b9-3690a7ad8fee\u002F5092.pdf",elocation_id:f,fpage:aH,article_id:K,viewed:493,downloaded:757,video_url:"https:\u002F\u002Fv1.oaepublish.com\u002Ffiles\u002Ftalkvideo\u002F5092.mp4",volume:aI,year:2022,tag:"223-43",image:"https:\u002F\u002Foaepublishstorage.blob.core.windows.net\u002F44befa84-3a12-4bd5-90b9-3690a7ad8fee\u002F5092-coverimg.jpg",authors:aJ,video_img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20240205\u002F06cb1187a7404f5e90abd019db7444b6.jpg",journal_path:m,lpage:243,author:aJ,specialissue:{id:1005,name:" Collaborative Optimization and Control of Intelligent Unmanned Autonomous Systems"},specialinfo:a,url_doi:M,image_list:"https:\u002F\u002Fimage.oaes.cc\u002F44befa84-3a12-4bd5-90b9-3690a7ad8fee\u002F5092-coverimg.jpg"},{date_published:1738857600,section:S,section_id:935,title:"Task cognition and planning for service robots",doi:"10.20517\u002Fir.2025.08",abstract:"\u003Cp\u003EWith the rapid development of artificial intelligence and robotics, service robots are increasingly becoming a part of our daily lives to provide domestic services. For robots to complete such services intelligently and with high quality, the prerequisite is that they can recognize and plan tasks to discover task requirements and generate executable action sequences. In this context, this paper systematically reviews the latest research progress in task cognition and planning for domestic service robots, covering key technologies such as command text parsing, active task cognition (ATC), multimodal perception, and action sequence generation. Initially, the challenges traditional rule-based command parsing methods face are analyzed, and the enhancement of robots’ understanding of complex instructions through deep learning methods is explored. Subsequently, the research trends in ATC are introduced, discussing the ability of robots to autonomously discover tasks by perceiving the surrounding environment through visual and semantic features. The discussion then moves to the current typical methods in task planning, comparing and analyzing four common approaches to highlight their advantages and disadvantages in this field. Finally, the paper summarizes the challenges of existing research and the future directions for development, providing references for further enhancing the task execution capabilities of domestic service robots in complex home environments.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F8725948d-9e72-44b9-b975-58656279e74b\u002Fir5008.pdf",elocation_id:f,fpage:119,article_id:7691,viewed:d,downloaded:d,video_url:"https:\u002F\u002Fv.oaes.cc\u002Fuploads\u002F20250207\u002F63f930aa71ab4ff78cbb1fac22a561be.mp4",volume:s,year:t,tag:"119-42",image:"https:\u002F\u002Foaepublishstorage.blob.core.windows.net\u002F8725948d-9e72-44b9-b975-58656279e74b\u002Fir5008-coverimg.jpg",authors:aK,video_img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20250207\u002F298da598f3d34f8c8b53bea9d9a09ef5.png",journal_path:m,lpage:142,author:aK,specialissue:a,specialinfo:a,url_doi:"ir.2025.08",image_list:"https:\u002F\u002Fimage.oaes.cc\u002F8725948d-9e72-44b9-b975-58656279e74b\u002Fir5008-coverimg.jpg"},{date_published:1738684800,section:p,section_id:i,title:"SKPNet: snake KAN perceive bridge cracks through semantic segmentation",doi:"10.20517\u002Fir.2025.07",abstract:"\u003Cp\u003EAs the demands for ensuring bridge safety continue to rise, crack detection technology has become more crucial than ever. In this context, deep learning methods have been widely applied in the field of intelligent crack detection for bridges. However, existing methods are often constrained by complex backgrounds and computational limitations, struggling with issues such as weak crack continuity and insufficient detail representation. Inspired by biological mechanisms, a dynamic snake convolution (DSC) with tubular offsets is incorporated to tackle these challenges effectively. Additionally, a channel-wise self-attention (CWSA) mechanism is introduced to efficiently fuse multi-scale features in U-Net, significantly enhancing the ability of the model to capture fine details. In the classification head, the traditional linear layer is replaced with a Kolmogorov-Arnold network (KAN) structure, which strengthens the robustness and generalization capacity of the model. Experimental results demonstrate that the proposed model improves detection accuracy, achieving a mean intersection over union (mIoU) of 0.877, while maintaining almost the same number of parameters, showcasing exceptional performance and practical applicability. Our project is released at \u003Ca target=\"_blank\" href=\"https:\u002F\u002Fgithub.com\u002Fruanyudi\u002FKanSeg-Bi\" xmlns:xlink=\"http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink\"\u003Ehttps:\u002F\u002Fgithub.com\u002Fruanyudi\u002FKanSeg-Bi\u003C\u002Fa\u003E.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002Fba9dde04-8e35-4852-b204-afac598834ad\u002Fir5007.pdf",elocation_id:f,fpage:105,article_id:7712,viewed:d,downloaded:d,video_url:"https:\u002F\u002Fv.oaes.cc\u002Fuploads\u002F20250205\u002F8f7e8f9e9a82401c8f54cc376d8c36d6.mp4",volume:s,year:t,tag:"105-18",image:q,authors:aL,video_img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20250205\u002F7c46da16b753459a90f72419852df9dc.png",journal_path:m,lpage:118,author:aL,specialissue:a,specialinfo:a,url_doi:"ir.2025.07"},{date_published:aM,section:p,section_id:i,title:"Stackelberg game-based anti-disturbance control for unmanned surface vessels via integrative reinforcement learning",doi:"10.20517\u002Fir.2025.06",abstract:"\u003Cp\u003EIn the navigation of unmanned surface vessels (USVs), external disturbances, particularly ocean waves, frequently induce deviations from the desired trajectory. To mitigate these challenges, we propose a novel disturbance rejection control strategy based on Stackelberg game theory, designed to address unmodeled system dynamics, complex environmental conditions, and other external perturbations. This approach incorporates several key innovations. First, we introduce a velocity error dynamic system coupled with a non-cooperative Stackelberg game model, where the USV's control inputs (as the leader) and external disturbances (as the follower) interact within an alternating update framework. This leader-follower interaction facilitates the joint optimization of both the disturbance rejection and performance-optimal control strategies, enhancing the USV's tracking accuracy while maximizing its disturbance rejection capacity. Second, we rigorously verify the existence of a cooperative optimal solution through an analysis of the Nash equilibrium under sequential decision-making between the leader and follower. Building on this, integral reinforcement learning and neural networks are employed to approximate the optimal Stackelberg solution. The boundedness and convergence of the proposed approach are validated using Lyapunov functions, ensuring stability and optimal performance under dynamic operating conditions. Finally, simulation results confirm the efficacy of the proposed strategy, demonstrating its ability to concurrently optimize control robustness and performance - such as minimizing tracking error and energy consumption - when confronted with unmodeled dynamics and external disturbances.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002Fc3a967a3-ac3d-471f-85b5-e34b251968a3\u002Fir5006.pdf",elocation_id:f,fpage:88,article_id:7680,viewed:d,downloaded:d,video_url:f,volume:s,year:t,tag:"88-104",image:"https:\u002F\u002Foaepublishstorage.blob.core.windows.net\u002Fc3a967a3-ac3d-471f-85b5-e34b251968a3\u002Fir5006-coverimg.jpg",authors:aN,video_img:a,journal_path:m,lpage:104,author:aN,specialissue:a,specialinfo:a,url_doi:"ir.2025.06",image_list:"https:\u002F\u002Fimage.oaes.cc\u002Fc3a967a3-ac3d-471f-85b5-e34b251968a3\u002Fir5006-coverimg.jpg"},{date_published:aM,section:p,section_id:i,title:"A novel real-time intelligent detector for monitoring UAVs in live-line operation on 10 kV distribution networks",doi:"10.20517\u002Fir.2025.05",abstract:"\u003Cp\u003EThe live-line operation of 10 kV distribution networks is critical for ensuring uninterrupted and high-quality power supply. However, operational sites face challenges such as insufficient intelligent monitoring and suboptimal realtime performance. To address these issues, this study proposes the FEM-YOLOv8 algorithm, specifically designed for protective equipment detection in live-line operation scenarios. The proposed algorithm is deployed on edge devices compatible with unmanned aerial vehicles (UAVs), enabling remote, autonomous, and intelligent monitoring. Key improvements include the introduction of an enhanced FAST-C2f module, replacing the original C2f module in the Backbone to improve feature extraction efficiency while reducing model complexity. Additionally, a lightweight efficient channel attention (ECA) mechanism is incorporated into the Backbone and Neck to enhance target feature detection and representation capabilities. The bounding box regression loss function is replaced with metric preserving distance intersection over union (MPDIoU) to further boost detection accuracy and robustness. The FEM-YOLOv8 model is implemented on the Atlas 200I DK A2 edge device, which is suitable for UAV deployment. Experimental results demonstrate that the improved FEM-YOLOv8 model achieves 93.1% precision (P), 85.9% recall (R), and 92.3% mean average precision (mAP), surpassing the baseline model by 2.8, 3.2, and 2.2 percentage points, respectively. With a detection speed of 83 frames per second (FPS) and a power consumption of only 10.2 W, the model satisfies real-time performance and detection accuracy requirements, providing significant contributions to grid intelligence and power operation safety.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F70d593d9-d1fe-4b5c-8b57-5a56eef2bc19\u002Fir5005.pdf",elocation_id:f,fpage:70,article_id:7679,viewed:d,downloaded:d,video_url:f,volume:s,year:t,tag:"70-87",image:q,authors:aO,video_img:a,journal_path:m,lpage:aE,author:aO,specialissue:a,specialinfo:a,url_doi:"ir.2025.05"},{date_published:aP,section:p,section_id:i,title:"Adaptive variational empirical mode decomposition aware intelligent data-driven modeling for complex industrial processes",doi:"10.20517\u002Fir.2025.04",abstract:"\u003Cp\u003EDue to the strong noise, high dimensionality and time-varying characteristics of industrial process data, data-driven modeling faces challenges in feature extraction and model interpretability. To address these issues, this paper proposes a new prediction model based on adaptive variational empirical mode decomposition-guided (AVEMDG) graph convolutional networks (GCNs). First, each sensor signal is decomposed into high-frequency and low-frequency features using empirical mode decomposition (EMD) to effectively capture multi-band information. Second, the weights of these features are adaptively updated through variational inference (Ⅵ) combined with Bayesian reasoning to handle the importance and uncertainty of features. Next, the GCN is used to model the spatiotemporal dependencies in the sensor network and is trained using the reweighted feature data. Last, the proposed method is applied to the prediction of the melt viscosity index (MVI), a key performance indicator (KPI) of the actual polyester fiber polymerization process. Ablation study and comparative experiment are conducted to evaluate the contribution of each component and the generality of the proposed model. Experimental results show that this method can effectively improve the model prediction accuracy, thereby enhancing the interpretability of the soft sensor model and providing guidance for the production of industrial processes.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F00d1f5ad-b235-4833-965c-2a506355e761\u002Fir5004.pdf",elocation_id:f,fpage:aQ,article_id:7657,viewed:d,downloaded:d,video_url:f,volume:s,year:t,tag:"50-69",image:q,authors:aR,video_img:a,journal_path:m,lpage:69,author:aR,specialissue:{id:1912,name:" Performance Evaluation and Optimization for Intelligent Systems"},specialinfo:a,url_doi:"ir.2025.04"},{date_published:aP,section:p,section_id:i,title:"CMMF-Net: a generative network based on CLIP-guided multi-modal feature fusion for thermal infrared image colorization",doi:"10.20517\u002Fir.2025.03",abstract:"\u003Cp\u003EThermal infrared (TIR) images remain unaffected by variations in light and atmospheric conditions, which makes them extensively utilized in diverse nocturnal traffic scenarios. However, challenges pertaining to low contrast and absence of chromatic information persist. The technique of image colorization emerges as a pivotal solution aimed at ameliorating the fidelity of TIR images. This enhancement is conducive to facilitating human interpretation and downstream analytical tasks. Because of the blurred and intricate features of TIR images, extracting and processing their feature information accurately through image-based approaches alone becomes challenging for networks. Hence, we propose a multi-modal model that integrates text features from TIR images with image features to jointly perform TIR image colorization. A vision transformer (ViT) model will be employed to extract features from the original TIR images. Concurrently, we manually observe and summarize the textual descriptions of the images, and then input these descriptions into a pretrained contrastive language-image pretraining (CLIP) model to capture text-based features. These two sets of features will then be fed into a cross-modal interaction (CI) module to establish the relationship between text and image. Subsequently, the text-enhanced image features will be processed through a U-Net network to generate the final colorized images. Additionally, we utilize a comprehensive loss function to ensure the network's ability to generate high-quality colorized images. The effectiveness of the methodology put forward in this study is evaluated using the KAIST datasets. The experimental results vividly showcase the superior performance of our CMMF-Net method in comparison to other methodologies for the task of TIR image colorization.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F1997a399-bbf5-4cf0-9a45-50f55c7d7fea\u002Fir5003.pdf",elocation_id:f,fpage:34,article_id:7656,viewed:d,downloaded:d,video_url:f,volume:s,year:t,tag:"34-49",image:q,authors:aS,video_img:a,journal_path:m,lpage:49,author:aS,specialissue:{id:1922,name:" Applications of Generative Adversarial Networks in Computer Vision and Image Processing"},specialinfo:a,url_doi:"ir.2025.03"},{date_published:1736524800,section:p,section_id:i,title:"An improved artificial potential field method for multi-AGV path planning in ports",doi:"10.20517\u002Fir.2025.02",abstract:"\u003Cp\u003EAs global maritime transport rapidly advances, the demands for intelligent, safe, and efficient automated container ports have significantly increased. In this evolving landscape, multi-automated guided vehicle (AGV) systems have emerged as a critical element of port automation, playing an essential role. Within automated container terminals, quay cranes, AGVs, and yard cranes are the primary equipment for loading and unloading operations on ships. However, the complexity of simultaneously considering numerous practical factors and the intricate relationships among them has made optimization modeling in this area a challenging task. To tackle this challenge, we have developed a path optimization model for multi-AGV systems in port environments, based on an enhanced artificial potential field (APF) algorithm. This algorithm utilizes the initial states of AGVs, target locations, and obstacle information as inputs. It creates attractive forces near the target locations and repulsive forces around static obstacles. Moreover, a minimum safety distance between AGVs is established; when AGVs approach closer than this threshold, the algorithm introduces repulsive forces between them to prevent collisions. The algorithm dynamically recalculates the repulsive potential field in response to real-time feedback and changes in the environment, enabling continuous adjustment to the AGV paths and action plans. This iterative process continues until all AGVs reach their designated targets. The effectiveness of this algorithm has been validated through port environment simulations, demonstrating clear advantages in enhancing the safety and smoothness of multi-AGV path planning.\u003C\u002Fp\u003E",pdfurl:"https:\u002F\u002Ff.oaes.cc\u002Fxmlpdf\u002F4a69b848-a11f-4064-a72d-b9e73b24ccb0\u002Fir5002.pdf",elocation_id:f,fpage:19,article_id:7629,viewed:d,downloaded:d,video_url:f,volume:s,year:t,tag:"19-33",image:q,authors:aT,video_img:a,journal_path:m,lpage:33,author:aT,specialissue:{id:1852,name:" Intelligent, Safe, and Green Shipping-oriented Maritime Data Exploitation and Knowledge 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articles are preserved here permanently:",url:"https:\u002F\u002Fwww.portico.org\u002Fpublishers\u002Foae\u002F",img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20230911\u002F67d78ebf8c55485db6ae5b5b4bcda421.jpg"},follow:[{title:"LinkedIn",url:"https:\u002F\u002Fwww.linkedin.com\u002Fin\u002Fintelligence-robotics\u002F",icon:"icon-linkedin"},{title:"Twitter",url:bc,icon:"icon-tuite1"}],wechat_img:a,twitter:{url:bc,img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20230824\u002F5249ddabb6d642558c9843fba9283219.png"}},top:{path:n,pid:r,journal_img:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20250113\u002F159ddc46c12d440d82d12f7fc8013e88.jpg",journal_name:o,mpt:"40 days",issn:bb,indexing:{ESCI:"https:\u002F\u002Fwww.oaepublish.com\u002Fnews\u002Fir.852",Scopus:bd,"Google Scholar":"https:\u002F\u002Fscholar.google.com.hk\u002Fcitations?view_op=list_works&hl=zh-CN&hl=zh-CN&user=-Hx5OVYAAAAJ",Dimensions:"https:\u002F\u002Fapp.dimensions.ai\u002Fdiscover\u002Fpublication?and_facet_source_title=jour.1423782",Lens:"https:\u002F\u002Fwww.lens.org\u002Flens\u002Fsearch\u002Fscholar\u002Flist?p=0&n=10&s=date_published&d=%2B&f=false&e=false&l=en&authorField=author&dateFilterField=publishedYear&orderBy=%2Bdate_published&presentation=false&preview=true&stemmed=true&useAuthorId=false&publicationType.must=journal%20article&sourceTitle.must=Intelligence%20%26%20Robotics&publisher.must=OAE%20Publishing%20Inc."},editor:"Simon X. Yang",journal_rank:a,journal_flyer:"https:\u002F\u002Ff.oaes.cc\u002Findex_ad\u002Fflyer\u002FIR-flyer.pdf",qksearch:["Intelligence","Robotics","Reinforcement Learning","Machine Learning","Unmanned Vehicles","UAV"],sitetag:"Intell Robot",ad:[],colour_tag:"#0047bb",score:a,mobile_top_img:a,impact_factor:[{factor:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20240813\u002F49390c7e86ab40a58ee862e8c1af65ba.png",url:bd},{factor:"https:\u002F\u002Fi.oaes.cc\u002Fuploads\u002F20240506\u002Fea3d9071c35b4bf3982ffe25f1083620.png",url:a}],rgba:"rgb(0,71,187)",log_image:"https:\u002F\u002Fi.oaes.cc\u002Fupload\u002Fjournal_logo\u002Fir.png"},webinfo:{},searchKey:a,loading:u,appid:a,videoPlay:{show:R,href:a}},editer:{editList:{list:{}}},userdata:{showLogin:R,logined:R}},serverRendered:u,routePath:"\u002Farticles\u002Fir.2024.19",config:{_app:{basePath:be,assetsPath:be,cdnURL:"https:\u002F\u002Fg.oaes.cc\u002Foae\u002Fnuxt\u002F"}}}}("",7201,"1",0,"2",null,"[\"1\"]","3",927,"4","5","6","IR","ir","Intelligence & Robotics","Research Article","0",40,5,2025,true,"Hao","Zhang","[\"2\"]","7","8","9","Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review","\u003Cp\u003EThis paper reviews the application of distributed model predictive control (DMPC) for autonomous intelligent systems (AIS) with unmanned aerial vehicles (UAVs) and vehicle platoon systems. DMPC is an optimal control method that formulates and solves optimization problems to adjust control strategies by predicting future states based on system models while managing constraints, and this technique has been applied to an increasing number of industrial areas. As the essential parts of AIS, UAVs and vehicle platoon systems have received extensive attention in the civil, industrial, and military fields. DMPC has the ability to quickly solve optimization problems in real-time while taking into account the prediction of the future state of the system, which fits in well with the ability of AIS to predict the environment when making decisions, so the application of DMPC in AIS has a natural advantage. This paper first introduces the basic principles of DMPC and the theoretical results in multi-agent systems (MASs). It then reviews the application of DMPC methods to UAVs and vehicle platoon systems. Finally, the challenges of the existing methods are summarized to offer insights to advance the future development of DMPC in practical applications.\u003C\u002Fp\u003E",2024,6671,"Leveraging active queries in collaborative robotic mission planning","ir.2024.06",5898,"Robust distributed model predictive control of connected vehicle platoon against DoS attacks","ir.2023.19",5092,"ℋ\u003Csub\u003E∞\u003C\u002Fsub\u003E leader-following consensus of multi-agent systems with channel fading under switching topologies: a semi-Markov kernel approach","ir.2022.19","en","10","11","Contact Us",false,"Review",4,3,1328," Robot System Intelligentization and Application: Learning, Control and Decision","Peng Y, Yan H, Rao K, Yang P, Lv Y. Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review. \u003Ci\u003EIntell Robot\u003C\u002Fi\u003E 2024;4(3):293-317. http:\u002F\u002Fdx.doi.org\u002F10.20517\u002Fir.2024.19","Peng Y, Yan H, Rao K, Yang P, Lv Y. Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review. \u003Ci\u003EIntell Robot\u003C\u002Fi\u003E. 2024;4:293-317. http:\u002F\u002Fdx.doi.org\u002F10.20517\u002Fir.2024.19","Peng, Yang, Penghui Yang, and Yunkai Lv. 2024. \"Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review\" \u003Ci\u003EIntell Robot\u003C\u002Fi\u003E. 4, no.3: 293-317. http:\u002F\u002Fdx.doi.org\u002F10.20517\u002Fir.2024.19","Peng, Y.; Yan, H.; Rao, K.; Yang, P.; Lv, Y. Distributed model predictive control for unmanned aerial vehicles and vehicle platoon systems: a review. \u003Ci\u003EIntell. Robot.\u003C\u002Fi\u003E \u003Cb\u003E2024\u003C\u002Fb\u003E, \u003Ci\u003E4\u003C\u002Fi\u003E, 293-317. http:\u002F\u002Fdx.doi.org\u002F10.20517\u002Fir.2024.19","2024-03-18 00:00:00","Cyrille","Berger","cyrille.berger@liu.se","Patrick","Doherty","Piotr","Rudol","Mariusz","Wzorek","2023-07-25 00:00:00","Zeng","Zehua","Ye","[\"*\",\"1\"]","2111803109@zjut.edu.cn","Dan","Qun","Lu","2022-08-20 00:00:00","Haoyue","Yang","zhang_hao@tongji.edu.cn","Zhuping","Wang","Xuemei","Zhou","40","Distributed model predictive control, autonomous intelligent systems, multi-agent systems, unmanned aerial vehicles, vehicle platoon systems","12","13",87,"Cyrille Berger\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0003-3011-1505' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Cyrille Berger'\u003E\u003C\u002Fa\u003E, ... Mariusz Wzorek\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0003-2147-2114' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Mariusz Wzorek'\u003E\u003C\u002Fa\u003E","Hao Zeng, ... Qun Lu",223,2,"Haoyue Yang\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0001-8867-6504' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Haoyue Yang'\u003E\u003C\u002Fa\u003E, ... Xuemei Zhou","Yongcheng Cui, ... Simon X. Yang\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0002-6888-7993' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Simon X. Yang'\u003E\u003C\u002Fa\u003E","Yudi Ruan, ... Xianyi Yang",1737388800,"Yizhen Meng, ... Guanbo Jing","Haibo Duan, ... Qiushi Cui",1736956800,50,"Yujun Chen, ... Kairui Sheng","Qian Jiang, ... Xin Jin\u003Ca href='https:\u002F\u002Forcid.org\u002F0000-0003-2211-2006' target='_blank'\u003E\u003Cimg src='https:\u002F\u002Fi.oaes.cc\u002Fimages\u002Forcid.png' class='author_id' alt='Xin Jin'\u003E\u003C\u002Fa\u003E","Xinqiang Chen, ... Yuzheng Wu","About","Editorial Policies","Journals","Academic Talks","\u002Fir","5555","\u002Fir\u002Fcontact_us","Video Abstract Guidelines","\u002Fir\u002Fvideo_abstract_guidelines","2770-3541 (Online)","https:\u002F\u002Ftwitter.com\u002FOAE_IR","https:\u002F\u002Fwww.scopus.com\u002Fsourceid\u002F21101199351","\u002F"));</script><script src="https://g.oaes.cc/oae/nuxt/47b9fdf.js" defer></script><script src="https://g.oaes.cc/oae/nuxt/5b7fe78.js" defer></script><script src="https://g.oaes.cc/oae/nuxt/800bc65.js" defer></script><script src="https://g.oaes.cc/oae/nuxt/d5348f9.js" defer></script><script src="https://g.oaes.cc/oae/nuxt/7bf631b.js" defer></script> </body> </html> <div id="noIe" style="display: none;"> <style> #noIe { background: rgba(99, 125, 255, 1); width: 100%; height: 100vh; position: fixed; top: 0; left: 0; z-index: 999999; } #noIe .container { width: 802px; height: 594px; background: #ffffff; border-radius: 10px; position: absolute; left: 50%; margin-left: -401px; 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