CINXE.COM

Document Zbl 1536.93778 - zbMATH Open

<!doctype html> <html lang="en"> <head> <meta charset="utf-8"> <title>Document Zbl 1536.93778 - zbMATH Open</title> <meta name="viewport" content="width=device-width, minimum-scale=0.1, maximum-scale=5.0"> <meta name="robots" content="noarchive, noindex"> <meta name="referrer" content="origin-when-cross-origin"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap/v3.3.7/css/bootstrap-theme.min.css" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.css" rel="stylesheet" media="screen,print"> <link rel="stylesheet" href="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/css/bootstrap-select.min.css"> <link href="/static/css/smoothness/jquery-ui-1.10.1.custom.min.css" rel="stylesheet" media="screen"> <link href="/static/styles.css?v=20241024" rel="stylesheet" media="screen,print"> <link href="https://static.zbmath.org/zbMathJax/v0.1.38/zbmathjax.css" rel="stylesheet" media="screen,print"> <link rel="shortcut icon" href="/static/zbmath.ico"> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Organization", "url": "https://zbmath.org/", "logo": "https://zbmath.org/static/zbMATH.png" } </script> </head> <body> <div id="line"></div> <span id="clear" style="cursor: pointer;">&times;</span> <div id="page"> <div id="head"> <nav id="menu" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#zbnav" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <a class="navbar-brand" href="#"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open logo"> </a> </div> <div id="zbnav" class="collapse navbar-collapse"> <ul class="nav navbar-nav pages"> <li class="about"> <a href="/about/">About</a> </li> <li class="frequently-asked-questions"> <a href="/frequently-asked-questions/">FAQ</a> </li> <li class="general-help"> <a href="/general-help/">General Help</a> </li> <li class="reviewer-service"> <a href="https://zbmath.org/reviewer-service/" target="_self" >Reviewer Service</a> </li> <li> <a href="/tools-and-resources/">Tools &amp; Resources</a> </li> <li class="contact"> <a href="/contact/">Contact</a> </li> </ul> <ul class="nav navbar-nav navbar-right prefs"> <li class="preferences dropdown"> <a data-toggle="dropdown" href="#">Preferences <i class="caret"></i></a> <ul class="dropdown-menu preferences"> <li> <form id="preferences" class="navbar-form" method="post" action="/preferences/" onsubmit="return confirm('This website uses cookies for the purposes of storing preference information on your device. Do you agree to this?\n\nPlease refer to our Privacy Policy to learn more about our use of cookies.')" > <input type="hidden" name="path" value="/1536.93778?"> <span class=""> <label class="title">Search Form</label> <div class="form-group"> <input id="search-multi-line" type="radio" name="search" value="multi-line" checked> <label for="search-multi-line" class="radio">Multi-Line Search (default)</label> </div> <div class="form-group"> <input id="search-one-line" type="radio" name="search" value="one-line"> <label for="search-one-line" class="radio">One-Line Search</label> </div> </span> <span class="count"> <label class="title">Hits per Page</label> <div class="form-group"> <input id="count-10" type="radio" name="count" value="10"> <label for="count-10" class="radio">10</label> </div> <div class="form-group"> <input id="count-20" type="radio" name="count" value="20"> <label for="count-20" class="radio">20</label> </div> <div class="form-group"> <input id="count-50" type="radio" name="count" value="50"> <label for="count-50" class="radio">50</label> </div> <div class="form-group"> <input id="count-100" type="radio" name="count" value="100" checked> <label for="count-100" class="radio">100 (default)</label> </div> <div class="form-group"> <input id="count-200" type="radio" name="count" value="200"> <label for="count-200" class="radio">200</label> </div> </span> <span class="format"> <label class="title">Display Format</label> <div class="form-group"> <input id="format-mathjax" type="radio" name="format" value="mathjax" checked> <label for="format-mathjax" class="radio">MathJax (default)</label> </div> <div class="form-group"> <input id="format-amstex" type="radio" name="format" value="latex"> <label for="format-amstex" class="radio">LaTeX</label> </div> </span> <span class="ranking"> <label class="title">Documents Sorting</label> <div class="form-group"> <input id="documents-ranking-default" type="radio" name="documents_ranking" value="date" checked> <label for="documents-ranking-default" class="radio">Newest first (default)</label> </div> <div class="form-group"> <input id="documents-ranking-references" type="radio" name="documents_ranking" value="references"> <label for="documents-ranking-references" class="radio">Citations</label> </div> <div class="form-group"> <input id="documents-ranking-relevance" type="radio" name="documents_ranking" value="relevance"> <label for="documents-ranking-relevance" class="radio">Relevance</label> </div> </span> <span class="ranking"> <label class="title">Authors Sorting</label> <div class="form-group"> <input id="authors-ranking-default" type="radio" name="authors_ranking" value="alpha" checked> <label for="authors-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="authors-ranking-references" type="radio" name="authors_ranking" value="references"> <label for="authors-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Serials Sorting</label> <div class="form-group"> <input id="serials-ranking-default" type="radio" name="serials_ranking" value="alpha" checked> <label for="serials-ranking-default" class="radio">Alphabetically (default)</label> </div> <div class="form-group"> <input id="serials-ranking-references" type="radio" name="serials_ranking" value="references"> <label for="serials-ranking-references" class="radio">Citations</label> </div> </span> <span class="ranking"> <label class="title">Software Sorting</label> <div class="form-group"> <input id="software-ranking-default" type="radio" name="software_ranking" value="references" checked> <label for="software-ranking-default" class="radio">Citations (default)</label> </div> <div class="form-group"> <input id="software-ranking-alpha" type="radio" name="software_ranking" value="alpha"> <label for="software-ranking-alpha" class="radio">Alphabetically</label> </div> </span> <button type="submit" class="btn btn-default">OK</button> <div class="clearfix"> </form> </li> </ul> </li> </ul> </div> </div> </nav> <div id="tabs"> <h1 class="logo"> <a class="logo" href="/"> <img class="logo" src="/static/zbmath.gif" alt="zbMATH Open &mdash; the first resource for mathematics" > </a> </h1> <nav> <ul class="nav nav-tabs"> <li class="tab-documents active"> <a href="/">Documents</a> </li> <li class="tab-authors"> <a href="/authors/">Authors</a> </li> <li class="tab-serials"> <a href="/serials/">Serials</a> </li> <li class="tab-software"> <a href="/software/">Software</a> </li> <li class="tab-classification"> <a href="/classification/">Classification</a> </li> <li class="tab-formulae"> <a href="/formulae/">Formulæ</a> </li> </ul> </nav> <div class="clearfix"></div> </div> <div class="content-fixed"> <div class="content-formular"> <div style="display: none;"> <div class="row ml-0"id="multi-line-new-line" style="display: none;"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-0-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-0-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input"> <span class="multi-line-value" id="multi-line-type-range"><span style="padding-left: 5px;">from</span> <input name="ml-0-v1" class="form-control multi-line-input" type="text" value="" aria-label="value"> until <input name="ml-0-v2" class="form-control multi-line-input" type="text" value="" aria-label="value"></span> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-la" placeholder="use name or ISO code"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-rv" placeholder="enter name or zbMATH reviewer number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-an" placeholder="Zbl, JFM or ERAM number"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-en" placeholder="e.g. DOI, ISBN, arXiv ID"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-sw" placeholder="use * to find all documents using software"> <input name="ml-0-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value" id="multi-line-type-input-br" placeholder="find documents about the life or work of a person"> <span class="multi-line-value" id="multi-line-type-multiselect-db"> <select class="multi-line-selectpicker" data-width="100%" multiple> <option value="zbl">Zbl</option> <option value="arxiv">arXiv</option> <option value="jfm">JFM</option> <option value="eram">ERAM</option> </select> <input type="hidden" class="multi-line-input" name="ml-0-v" value=""> </span> </div> <form name="documents" method="GET" action="/" autocomplete="off"> <div class="documents multi-line" style="display: none;"> <div class="forms"> <ul class="nav forms"> <li class="one-line"> <span tabindex="0" class="glyphicon glyphicon-question-sign" title="One-Line Search allows for free logical combinations of search fields" aria-label="One-Line Search allows for free logical combinations of search fields" data-placement="bottom"></span>&nbsp;<a style="display: inline-block;" href="#">One-Line Search <span class="glyphicon glyphicon-search"></span></a> </li> </ul> </div> <div class="clearfix"></div> <div class="container-fluid"> <input type="hidden" id="multi-line-ml" name="ml" value="3"> <div id="multi-line-row-wrapper"> <div class="row ml-1"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-1-f" aria-label="field"> <option data-type="input" value="any" selected>Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-1-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-1-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-2"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-2-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au" selected>Authors</option> <option data-type="input" value="ti">Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-2-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><select class="form-control multi-line-operators multi-line-selectpicker" name="ml-2-op" aria-label="operator"> <option value="and" selected>AND</option> <option value="andnot">AND NOT</option> <option value="or">OR</option> </select></div> </div> <div class="row ml-3"> <div class="col-xs-12 form-inline multi-line"> <select class="form-control multi-line-field multi-line-selectpicker" name="ml-3-f" aria-label="field"> <option data-type="input" value="any">Anywhere</option> <option data-type="input" value="au">Authors</option> <option data-type="input" value="ti" selected>Title</option> <option data-type="input" value="py">Year</option> <option data-type="range" value="pyr">Year Range</option> <option data-type="input" value="cc">MSC</option> <option data-type="input" value="cc1">MSC Primary</option> <option data-type="input" value="so">Source / Journal</option> <option data-type="input" value="pu">Publisher</option> <option data-type="input" value="la">Language</option> <option data-type="input" value="ab">Summary / Review</option> <option data-type="input" value="rv">Reviewer</option> <option data-type="input" value="an">zbMATH ID</option> <option data-type="input" value="en">External ID</option> <option data-type="input" value="ut">Keywords</option> <option data-type="input" value="sw">Software</option> <option data-type="input" value="br">Biographic Ref</option> <option data-type="input" value="rft">Reference Text</option> <option data-type="multiselect-db" value="db">Database</option> <option data-divider="true"></option> <option data-function="remove-line" data-content='<span class="glyphicon glyphicon-minus" aria-hidden="true"></span> remove line' value="any">remove line</option> </select><input name="ml-3-v" class="form-control multi-line-value multi-line-input" type="text" value="" aria-label="value"><div id="multi-line-plus"> <a href="#"><span class="glyphicon glyphicon-plus" aria-hidden="true"></span> add line</a> </div></div> </div> </div> <div class="row"> <div class="col-xs-12 form-inline"> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-test" style="visibility: hidden; position: fixed;"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label title="search for Articles in Journals"> <input type="checkbox" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label title="search for arXiv Preprints"> <input type="checkbox" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> <div class="form-group field checkboxes-wrapper" id="checkboxes-wrapper-real"> <label>Document Type:</label> <div class="checkboxes"> <div class="slider"> <label for="dt-j" title="search for Articles in Journals"> <input type="checkbox" id="dt-j" name="dt" class="form-control" value="j" checked> <span tabindex="0"><small></small></span> Journal Articles </label> </div> <div class="slider"> <label for="dt-a" title="search for Articles in Conference Proceedings and Collected Volumes"> <input type="checkbox" id="dt-a" name="dt" class="form-control" value="a" checked> <span tabindex="0"><small></small></span> Collection Articles </label> </div> <div class="slider"> <label for="dt-b" title="search for Monographs, Proceedings, Dissertations etc."> <input type="checkbox" id="dt-b" name="dt" class="form-control" value="b" checked> <span tabindex="0"><small></small></span> Books </label> </div> <div class="slider"> <label for="dt-p" title="search for arXiv Preprints"> <input type="checkbox" id="dt-p" name="dt" class="form-control" value="p" checked> <span tabindex="0"><small></small></span> arXiv Preprints </label> </div> </div> </div> </div> </div> <div class="row"> <div class="col-xs-12 buttons"> <a tabindex="0" class="btn btn-default clear-all">Reset all <span class="glyphicon glyphicon-remove"></span></a> <div class="submit"> <button class="btn btn-default search" type="submit">Search <span class="glyphicon glyphicon-search"></span></button> </div> </div> </div> </div> </div> </form> <form class="form-inline" name="documents" method="GET" action="/"> <div class="documents one-line" style="display: block;"> <div class="forms"> <ul class="nav forms"> <li class="multi-line"><a href="#">New Multi-Line Search <span class="glyphicon glyphicon-list"></span></a></li> </ul> </div> <div id="search-row" class="input-group box"> <span> <div id="search-field"> <input class="query form-control" type="text" name="q" value="an:1536.93778" aria-label="Search for documents" placeholder="Search for documents" autocomplete="off"> </div> <div class="search-buttons input-group-btn"> <div class="btn-group"> <button class="btn btn-default search" type="submit"><span class="virtual">Search</span> <span class="glyphicon glyphicon-search" style="top: 2px;"></span></button> </div> </div> </span> <span> <div class="search-buttons input-group-btn"> <div class="btn-group"> <div class="btn-group fields"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Fields <i class="caret"></i></button> <ul id="fields" class="dropdown-menu pull-right"> <li><a href="#"><span class="token item">any:</span><span>&nbsp;</span>anywhere (default)</a></li> <li><a href="#"><span class="token item">ab:</span><span>&nbsp;&nbsp;</span>review text</a></li> <li><a href="#"><span class="token item">an:</span><span>&nbsp;&nbsp;</span>zbmath id</a></li> <li><a href="#"><span class="token item">any:</span><span>&nbsp;&nbsp;</span>anywhere</a></li> <li><a href="#"><span class="token item">au:</span><span>&nbsp;&nbsp;</span>contributor name</a></li> <li><a href="#"><span class="token item">br:</span><span>&nbsp;&nbsp;</span>biographic reference name</a></li> <li><a href="#"><span class="token item">cc:</span><span>&nbsp;&nbsp;</span>msc title</a></li> <li><a href="#"><span class="token item">dt:</span><span>&nbsp;&nbsp;</span>document type</a></li> <li><a href="#"><span class="token item">doi:</span><span>&nbsp;&nbsp;</span>doi</a></li> <li><a href="#"><span class="token item">en:</span><span>&nbsp;&nbsp;</span>external id</a></li> <li><a href="#"><span class="token item">la:</span><span>&nbsp;&nbsp;</span>language</a></li> <li><a href="#"><span class="token item">pu:</span><span>&nbsp;&nbsp;</span>publisher</a></li> <li><a href="#"><span class="token item">py:</span><span>&nbsp;&nbsp;</span>year</a></li> <li><a href="#"><span class="token item">rv:</span><span>&nbsp;&nbsp;</span>reviewer name</a></li> <li><a href="#"><span class="token item">so:</span><span>&nbsp;&nbsp;</span>source</a></li> <li><a href="#"><span class="token item">sw:</span><span>&nbsp;&nbsp;</span>software name</a></li> <li><a href="#"><span class="token item">ti:</span><span>&nbsp;&nbsp;</span>title</a></li> <li><a href="#"><span class="token item">ut:</span><span>&nbsp;&nbsp;</span>keyword</a></li> </ul> </div> <div class="btn-group operators"> <button class="btn btn-default dropdown-toggle" data-toggle="dropdown">Operators <i class="caret"></i></button> <ul id="operators" class="dropdown-menu pull-right"> <li><a href="#"><span class="token">a&nbsp;<span class="item">&</span>&nbsp;b&nbsp;</span><span>&nbsp;</span>logical and (default)</a></li> <li><a href="#"><span class="token">a&nbsp;<span class="item">|</span>&nbsp;b&nbsp;</span><span>&nbsp;</span>logical or</a></li> <li><a href="#"><span class="token"><span class="item">!</span>ab&nbsp;&nbsp;&nbsp;</span><span>&nbsp;</span>logical not</a></li> <li><a href="#"><span class="token">abc<span class="item">*</span>&nbsp;&nbsp;</span><span>&nbsp;</span>right wildcard</a></li> <li><a href="#"><span class="token"><span class="item">"</span>ab&nbsp;c<span class="item">"</span></span><span>&nbsp;</span>phrase</a></li> <li><a href="#"><span class="token"><span class="item">(</span>ab&nbsp;c<span class="item">)</span></span><span>&nbsp;</span>parentheses</a></li> </ul> </div> </div> </div> <div class="special"> <ul class="nav help-button"> <li class="dropdown pull-right"> <a href="#">Help <i class="caret"></i></a> </li> </ul> </div> </span> </div> <div class="help"><h2>Examples</h2> <div id="help-terms" role="table"> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Geometry">Geometry</a></span> <span class="search-explanation" role="cell" role="cell">Search for the term <em>Geometry</em> in <strong>any</strong> field. Queries are <strong>case-independent</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Funct%2A">Funct*</a></span> <span class="search-explanation" role="cell"><strong>Wildcard</strong> queries are specified by <strong><u>*</u></strong> (e.g. <em>functions</em>, <em>functorial</em>, etc.). Otherwise the search is <strong>exact</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Topological+group%22">"Topological group"</a></span> <span class="search-explanation" role="cell"><strong>Phrases</strong> (multi-words) should be set in <u>"</u>straight quotation marks<u>"</u>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=au%3A+Bourbaki+%26+ti%3A+Algebra">au: Bourbaki &amp; ti: Algebra</a></span> <span class="search-explanation" role="cell">Search for <strong><u>au</u>thor</strong> and <strong><u>ti</u>tle</strong>. The <strong>and-operator &amp;</strong> is default and can be omitted.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Chebyshev+%7C+Tschebyscheff">Chebyshev | Tschebyscheff</a></span> <span class="search-explanation" role="cell">The <strong>or-operator |</strong> allows to search for <em>Chebyshev</em> or <em>Tschebyscheff</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=Quasi%2A+map%2A+py%3A+1989">Quasi* map* py: 1989</a></span> <span class="search-explanation" role="cell">The resulting documents have <strong><u>p</u>ublication <u>y</u>ear</strong> <em>1989</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=so%3A+Eur%2A+J%2A+Mat%2A+Soc%2A+cc%3A+14">so: Eur* J* Mat* Soc* cc: 14</a></span> <span class="search-explanation" role="cell">Search for publications in a particular <strong><u>so</u>urce</strong> with a <strong>Mathematics Subject <u>C</u>lassification <u>c</u>ode (<u>cc</u>)</strong> in <em>14</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=%22Partial+diff%2A+eq%2A%22+%21+elliptic">"Partial diff* eq*" ! elliptic</a></span> <span class="search-explanation" role="cell">The <strong>not</strong>-operator <strong>!</strong> eliminates all results containing the word <em>elliptic</em>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=dt%3A+b+%26+au%3A+Hilbert">dt: b &amp; au: Hilbert</a></span> <span class="search-explanation" role="cell">The <strong><u>d</u>ocument <u>t</u>ype</strong> is set to books; alternatively: <u>j</u> for <strong>journal articles</strong>, <u>a</u> for <strong>book articles</strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=py%3A+2000-2015+cc%3A+%2894A+%7C+11T%29">py: 2000-2015 cc: (94A | 11T)</a></span> <span class="search-explanation" role="cell">Number <strong>ranges</strong> are accepted. Terms can be grouped within <strong><u>(</u>parentheses<u>)</u></strong>.</span> </div> <div class="help-item" role="row"> <span class="search-example" role="rowheader"><a href="/?q=la%3A+chinese">la: chinese</a></span> <span class="search-explanation" role="cell">Find documents in a given <strong><u>la</u>nguage</strong>. <a href="http://en.wikipedia.org/wiki/ISO_639-1">ISO 639-1</a> language codes can also be used.</span> </div> </div> <div id="help-fields"> <h2>Fields</h2> <table> <tr> <td class="nowrap padding" role="rowheader"><strong>any</strong></td> <td class="padding">anywhere</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>an</strong></td> <td class="padding">internal document identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>au</strong></td> <td class="padding">author, editor</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ai</strong></td> <td class="padding">internal author identifier</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ti</strong></td> <td class="padding">title</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>la</strong></td> <td class="padding">language</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>so</strong></td> <td class="padding">source</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ab</strong></td> <td class="padding">review, abstract</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>py</strong></td> <td class="padding">publication year</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>rv</strong></td> <td class="padding">reviewer</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>cc</strong></td> <td class="padding">MSC code</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>ut</strong></td> <td class="padding">uncontrolled term</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>dt</strong></td> <td class="padding" colspan="4">document type (<strong>j</strong>: journal article; <strong>b</strong>: book; <strong>a</strong>: book article)</td> </tr> </table> </div> <div id="help-operators"> <h2>Operators</h2> <table> <tr> <td class="nowrap padding" role="rowheader">a <strong>&amp;</strong> b</td> <td class="padding">logic and</td> </tr> <tr> <td class="nowrap padding" role="rowheader">a <strong>|</strong> b</td> <td class="padding">logic or</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>!</strong>ab</td> <td class="padding">logic not</td> </tr> <tr> <td class="nowrap padding" role="rowheader">abc<strong>*</strong></td> <td class="padding">right wildcard</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>"</strong>ab c<strong>"</strong></td> <td class="padding">phrase</td> </tr> <tr> <td class="nowrap padding" role="rowheader"><strong>(</strong>ab c<strong>)</strong></td> <td class="padding">parentheses</td> </tr> </table> </div> <p> See also our <a href="/general-help/">General Help</a>. </p></div> </div> </form> <div class="clearfix"></div> </div> <div class="content-shadow"></div> </div> </div> <div id="body"> <div id="main"> <div class="messages"> </div> <div id="documents"> <div class="content-main"> <div class="content-item"><div class="item"> <article> <div class="author"><a href="/authors/wei.shuyi" title="Author Profile">Wei, Shu-Yi</a>; <a href="/authors/li.yuanxin" title="Author Profile">Li, Yuan-Xin</a></div> <h2 class="title"> <strong>Finite-time adaptive neural network command filtered controller design for nonlinear system with time-varying full-state constraints and input quantization.</strong> <i>(English)</i> <a class="label nowrap" href="/1536.93778">Zbl 1536.93778</a> </h2> <div class="source"> <a href="/serials/454" title="Journal Profile">Inf. Sci.</a> <a href="/?q=in%3A510974" title="Articles in this Issue">613, 871-887 (2022)</a>. </div> <div class="abstract">Summary: In this paper, an adaptive finite-time command filtered control scheme is investigated for a class of nonlinear systems with asymmetric time-varying full state constraints and input quantization. Firstly, by fusing the backstepping control method and command filter technique, a novel adaptive neural networks (NNs) command filtered control approach is proposed. Moreover, a modified error compensation mechanism is constructed to compensate for the filtering error. Secondly, a smooth nonlinear transformation is constructed to eliminate the influence brought by the actuator subject to input quantization. Based on the constructed asymmetric time-varying barrier Lyapunov function (TVBLF), the strict constraints are guaranteed not to be violated and the stability of the closed-loop system is achieved in finite-time. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7830727">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D40" title="MSC2020">93D40</a> </td> <td class="space"> Finite-time stability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C40" title="MSC2020">93C40</a> </td> <td class="space"> Adaptive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E11" title="MSC2020">93E11</a> </td> <td class="space"> Filtering in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D30" title="MSC2020">93D30</a> </td> <td class="space"> Lyapunov and storage functions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Auncertain+nonlinear+systems">uncertain nonlinear systems</a>; <a href="/?q=ut%3Acommand+filtered+backstepping">command filtered backstepping</a>; <a href="/?q=ut%3Ainput+quantization">input quantization</a>; <a href="/?q=ut%3Aadaptive+control">adaptive control</a>; <a href="/?q=ut%3Atime-varying+barrier+Lyapunov+function">time-varying barrier Lyapunov function</a>; <a href="/?q=ut%3Afinite-time+convergence">finite-time convergence</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1536.93778" data-ciurl="/ci/07830727" data-biburl="/bibtex/07830727.bib" data-amsurl="/amsrefs/07830727.bib" data-xmlurl="/xml/07830727.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07830727.pdf" title="Zbl 1536.93778 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1016/j.ins.2022.08.114" aria-label="DOI for “Finite-time adaptive neural network command filtered controller design for nonlinear system with time-varying full-state constraints and input quantization”" title="10.1016/j.ins.2022.08.114">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bhat, S. P.; Bernstein, D. S., Continuous finite-time stabilization of the translational and rotational double integrators, IEEE Transactions on Automatic Control, 43, 678-682 (1998) &middot; <a href="/0925.93821" class="nowrap">Zbl 0925.93821</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, L.; Li, C.; Sun, Y.; Ma, G., Distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with error constraints, International Journal of Control, 94, 3, 698-710 (2021) &middot; <a href="/1480.93361" class="nowrap">Zbl 1480.93361</a></td> </tr><tr> <td>[3]</td> <td class="space">Cui, Y.; Liu, X.; Deng, X.; Wen, G., Command-filter-based adaptive finite-time consensus control for nonlinear strict-feedback multi-agent systems with dynamic leader, Information Sciences, 565, 17-31 (2021) &middot; <a href="/1530.93510" class="nowrap">Zbl 1530.93510</a></td> </tr><tr> <td>[4]</td> <td class="space">C. Deng, C. Wen, J. Huang, X.-M. Zhang, Y. Zou, Distributed observer-based cooperative control approach for uncertain nonlinear MASs under event-triggered communication, IEEE Transactions on Automatic Control doi:10.1109/TAC.2021.3090739. &middot; <a href="/1537.93382" class="nowrap">Zbl 1537.93382</a></td> </tr><tr> <td>[5]</td> <td class="space">Farrell, J. A.; Polycarpou, M.; Sharma, M.; Dong, W., Command filtered backstepping, IEEE Transactions on Automatic Control, 54, 1391-1395 (2009) &middot; <a href="/1367.93382" class="nowrap">Zbl 1367.93382</a></td> </tr><tr> <td>[6]</td> <td class="space">Feng, Y.; Wu, M.; Chen, L.; Chen, X.; Cao, W.; Du, S.; Pedrycz, W., Hybrid intelligent control based on condition identification for combustion process in heating furnace of compact strip production, IEEE Transactions on Industrial Electronics, 69, 3, 2790-2800 (2021)</td> </tr><tr> <td>[7]</td> <td class="space">Gao, H.; Song, Y.; Wen, C., Event-triggered adaptive neural network controller for uncertain nonlinear system, Information Sciences, 506, 148-160 (2020) &middot; <a href="/1460.93062" class="nowrap">Zbl 1460.93062</a></td> </tr><tr> <td>[8]</td> <td class="space">He, W.; Huang, H.; Ge, S. S., Adaptive neural network control of a robotic manipulator with time-varying output constraints, IEEE Transactions on Cybernetics, 47, 3136-3147 (2017)</td> </tr><tr> <td>[9]</td> <td class="space">Hong, Y.; Wang, J.; Cheng, D., Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE Transactions on Automatic Control, 51, 858-862 (2006) &middot; <a href="/1366.93290" class="nowrap">Zbl 1366.93290</a></td> </tr><tr> <td>[10]</td> <td class="space">Huang, X.; Lin, W.; Yang, B., Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 41, 881-888 (2005) &middot; <a href="/1098.93032" class="nowrap">Zbl 1098.93032</a></td> </tr><tr> <td>[11]</td> <td class="space">Lai, G.; Tao, G.; Zhang, Y.; Liu, Z., Adaptive control of noncanonical neural-network nonlinear systems with unknown input dead-zone characteristics, IEEE Transactions on Neural Networks and Learning Systems, 31, 9, 3346-3360 (2020)</td> </tr><tr> <td>[12]</td> <td class="space">Levant, A., Higher-order sliding modes, differentiation and output-feedback control, Automatica, 76, 924-941 (2003) &middot; <a href="/1049.93014" class="nowrap">Zbl 1049.93014</a></td> </tr><tr> <td>[13]</td> <td class="space">Y.X. Li, Command filter adaptive asymptotic tracking of uncertain nonlinear systems with time-varying parameters and disturbances, IEEE Transactions on Automatic Control doi: 10.1109/TAC.2021.3089626. &middot; <a href="/1537.93404" class="nowrap">Zbl 1537.93404</a></td> </tr><tr> <td>[14]</td> <td class="space">B. Liu, W. Wang, Y. Li, Y. Yi, G. Xie, Adaptive quantized predefined-time backstepping control for nonlinear strict-feedback systems, IEEE Transactions on Circuits and Systems II: Express Briefs doi:10.1109/TCSII.2022.3175739.</td> </tr><tr> <td>[15]</td> <td class="space">Li, M.; Chen, Y.; Liu, Y., Adaptive disturbance observer-based event-triggered fuzzy control for nonlinear system, Information, Science, 575, 485-498 (2021) &middot; <a href="/1530.93199" class="nowrap">Zbl 1530.93199</a></td> </tr><tr> <td>[16]</td> <td class="space">D. Li, H. Han, J. Qiao, Deterministic learning-based adaptive neural control for nonlinear full-state constrained systems, IEEE Transactions on Neural Networks and Learning Systems doi:10.1109/TNNLS.2021.3126320.</td> </tr><tr> <td>[17]</td> <td class="space">Li, Y. X.; Yang, G. H., Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults, Automatica, 72, 177-185 (2016) &middot; <a href="/1344.93061" class="nowrap">Zbl 1344.93061</a></td> </tr><tr> <td>[18]</td> <td class="space">Y. Li, Y. Liu, S. Tong, Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints, IEEE Transactions on Neural Networks and Learning Systems doi: 10.1109/TNNLS.2021.3051030.</td> </tr><tr> <td>[19]</td> <td class="space">Liu, Y. J.; Gong, M.; Tong, S.; Chen, C. P.; Li, D. J., Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints, IEEE Transactions on Fuzzy Systems, 26, 2607-2617 (2018)</td> </tr><tr> <td>[20]</td> <td class="space">Liu, C.; Liu, X.; Wang, H.; Zhou, Y.; Lu, S., Finite-time adaptive tracking control for unknown nonlinear systems with a novel barrier Lyapunov function, Information Sciences, 528, 231-245 (2020) &middot; <a href="/1461.93454" class="nowrap">Zbl 1461.93454</a></td> </tr><tr> <td>[21]</td> <td class="space">Y. Liu, Q. Zhu, Adaptive fuzzy finite-time control for nonstrict-feedback nonlinear systems, IEEE Transactions on Cybernetics doi:10.1109/TCYB.2021.3063139.</td> </tr><tr> <td>[22]</td> <td class="space">Liu, Y. J.; Ma, L.; Liu, L.; Tong, S.; Chen, C. P., Adaptive neural network learning controller design for a class of nonlinear systems with time-varying state constraints, IEEE Transactions on Neural Networks and Learning Systems, 31, 66-75 (2019)</td> </tr><tr> <td>[23]</td> <td class="space">S. Lu, M. Chen, Y. Liu, S. Shao, Adaptive NN tracking control for uncertain MIMO nonlinear system with time-varying state constraints and disturbances, IEEE Transactions on Neural Networks and Learning Systems doi:10.1109/TNNLS.2022.3141052.</td> </tr><tr> <td>[24]</td> <td class="space">Ma, J.; Park, J. H.; Xu, S., Command-filter-based finite-time adaptive control for nonlinear systems with quantized input, IEEE Transactions on Automatic Control, 66, 2339-2344 (2020) &middot; <a href="/1536.93929" class="nowrap">Zbl 1536.93929</a></td> </tr><tr> <td>[25]</td> <td class="space">Y. Ma, W. Che, C. Deng, Z. Wu, Observer-based event-triggered containment control for MASs under DoS attacks, IEEE Transactions on Cybernetics doi:10.1109/TCYB.2021.3104178.</td> </tr><tr> <td>[26]</td> <td class="space">J. Ma, H. Wang, J. Qiao, Adaptive neural fixed-time tracking control for high-order nonlinear systems, IEEE Transactions on Neural Networks and Learning Systems doi:10.1109/TNNLS.2022.3176625.</td> </tr><tr> <td>[27]</td> <td class="space">Meng, B.; Liu, W.; Qi, X., Disturbance and state observer-based adaptive finite-time control for quantized nonlinear systems with unknown control directions, Journal of the Franklin Institute, 359, 7, 2906-2931 (2022) &middot; <a href="/1489.93109" class="nowrap">Zbl 1489.93109</a></td> </tr><tr> <td>[28]</td> <td class="space">Mobayen, S.; Mofid, O.; Din, S. U.; Bartoszewicz, A., Finite-time tracking controller design of perturbed robotic manipulator based on adaptive second-order sliding mode control method, IEEE Access, 9, 71159-71169 (2021)</td> </tr><tr> <td>[29]</td> <td class="space">Patel, R.; Hafiz, F.; Swain, A.; Ukil, A., Nonlinear excitation control of diesel generator: A command filter backstepping approach, IEEE Transactions on Industrial Informatics, 17, 4809-4817 (2020)</td> </tr><tr> <td>[30]</td> <td class="space">J. Sun, H. He, J. Yi, Z. Pu, Finite-time command-filtered composite adaptive neural control of uncertain nonlinear systems, IEEE Transactions on Cybernetics doi:10.1109/TCYB.2020.3032096.</td> </tr><tr> <td>[31]</td> <td class="space">Song, S.; Park, J. H.; Zhang, B.; Song, X., Composite adaptive fuzzy finite-time quantized control for full state-constrained nonlinear systems and its application, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52, 4, 2479-2490 (2021)</td> </tr><tr> <td>[32]</td> <td class="space">W. Sun, S.F. Su, J. Xia, G. Zhuang, Command filter-based adaptive prescribed performance tracking control for stochastic uncertain nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems doi:10.1109/TSMC.2019.2963220.</td> </tr><tr> <td>[33]</td> <td class="space">Sun, Y.; Chen, B.; Lin, C.; Wang, H., Finite-time adaptive control for a class of nonlinear systems with nonstrict feedback structure, IEEE Transactions on Cybernetics, 48, 2774-2782 (2017)</td> </tr><tr> <td>[34]</td> <td class="space">Tee, K. P.; Ge, S. S.; Tay, E. H., Barrier Lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45, 918-927 (2009) &middot; <a href="/1162.93346" class="nowrap">Zbl 1162.93346</a></td> </tr><tr> <td>[35]</td> <td class="space">Wang, H.; Liu, P. X.; Xie, X.; Liu, X.; Hayat, T.; Alsaadi, F. E., Adaptive fuzzy asymptotical tracking control of nonlinear systems with unmodeled dynamics and quantized actuator, Information Sciences, 575, 779-792 (2021) &middot; <a href="/1530.93216" class="nowrap">Zbl 1530.93216</a></td> </tr><tr> <td>[36]</td> <td class="space">Wang, K.; Liu, X.; Jing, Y., Command filtered finite-time control for nonlinear systems with state constraints and its application to TCP network, Information Sciences, 550, 189-206 (2021) &middot; <a href="/1485.93526" class="nowrap">Zbl 1485.93526</a></td> </tr><tr> <td>[37]</td> <td class="space">K. Wang, X. Liu, Y. Jing, Adaptive finite-time command filtered controller design for nonlinear systems with output constraints and input nonlinearities, IEEE Transactions on Neural Networks and Learning Systems doi:10.1109/TNNLS.2021.3083800.</td> </tr><tr> <td>[38]</td> <td class="space">Wang, B.; Iwasaki, M.; Yu, J., Command filtered adaptive backstepping control for dual-motor servo systems with torque disturbance and uncertainties, IEEE Transactions on Industrial Electronics, 69, 2, 1773-1781 (2021)</td> </tr><tr> <td>[39]</td> <td class="space">Xia, J.; Zhang, J.; Feng, J.; Wang, Z.; Zhuang, G., Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 1945-1953 (2019)</td> </tr><tr> <td>[40]</td> <td class="space">B. Xu, Y.X. Li, C.K. Ahn, Small-gain approach to fuzzy adaptive control for interconnected systems with unmodeled dynamics, IEEE Transactions on Fuzzy Systems doi:10.1109/TFUZZ.2022.3157038.</td> </tr><tr> <td>[41]</td> <td class="space">Xue, G.; Lin, F.; Li, S.; Liu, H., Adaptive fuzzy finite-time backstepping control of fractional-order nonlinear systems with actuator faults via command-filtering and sliding mode technique, Information Sciences, 600, 189-208 (2022) &middot; <a href="/1533.93393" class="nowrap">Zbl 1533.93393</a></td> </tr><tr> <td>[42]</td> <td class="space">Yu, X.; Lin, Y., Adaptive backstepping quantized control for a class of nonlinear systems, IEEE Transactions on Automatic Control, 62, 981-985 (2016) &middot; <a href="/1364.93353" class="nowrap">Zbl 1364.93353</a></td> </tr><tr> <td>[43]</td> <td class="space">Zamfirache, I. A.; Precup, R. E.; Roman, R. C.; Petriu, E. M., Reinforcement learning-based control using Q-learning and gravitational search algorithm with experimental validation on a nonlinear servo system, Information Sciences, 583, 99-120 (2022) &middot; <a href="/1532.93132" class="nowrap">Zbl 1532.93132</a></td> </tr><tr> <td>[44]</td> <td class="space">Zamfirache, I. A.; Precup, R. E.; Roman, R. C.; Petriu, E. M., Policy iteration reinforcement learning-based control using a grey wolf optimizer algorithm, Information Sciences, 585, 162-175 (2022) &middot; <a href="/07800116" class="nowrap">Zbl 07800116</a></td> </tr><tr> <td>[45]</td> <td class="space">L. Zhang, W.W. Che, B. Chen, Lin, C, Adaptive fuzzy output-feedback consensus tracking control of nonlinear multiagent systems in prescribed performance, IEEE Transactions on Cybernetics doi:10.1109/TCYB.2022.3171239.</td> </tr><tr> <td>[46]</td> <td class="space">Zhao, L.; Liu, G.; Yu, J., Finite-time adaptive fuzzy tracking control for a class of nonlinear systems with full-state constraints, IEEE Transactions on Fuzzy Systems, 29, 2246-2255 (2020)</td> </tr><tr> <td>[47]</td> <td class="space">Zheng, X.; Yang, X., Command filter and universal approximator based backstepping control design for strict-feedback nonlinear systems with uncertainty, IEEE Transactions on Automatic Control, 65, 1310-1317 (2019) &middot; <a href="/1533.93822" class="nowrap">Zbl 1533.93822</a></td> </tr><tr> <td>[48]</td> <td class="space">Zhou, J.; Wen, C.; Yang, G., Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal, IEEE Transactions on Automatic Control, 59, 2, 460-464 (2013) &middot; <a href="/1360.93626" class="nowrap">Zbl 1360.93626</a></td> </tr><tr> <td>[49]</td> <td class="space">Zhao, J.; Tong, S.; Li, Y., Fuzzy adaptive output feedback control for uncertain nonlinear systems with unknown control gain functions and unmodeled dynamics, Information Sciences, 558, 140-156 (2021) &middot; <a href="/1489.93065" class="nowrap">Zbl 1489.93065</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH&nbsp;Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> &copy; 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms &amp; Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none">&nbsp;<span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10