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href="https://az.wikipedia.org/wiki/Adaptiv_idar%C9%99etm%C9%99" title="Adaptiv idarəetmə – Azerbaijani" lang="az" hreflang="az" data-title="Adaptiv idarəetmə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Adaptive_Regelung" title="Adaptive Regelung – German" lang="de" hreflang="de" data-title="Adaptive Regelung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D9%86%D8%AA%D8%B1%D9%84_%D8%AA%D8%B7%D8%A8%DB%8C%D9%82%DB%8C" title="کنترل تطبیقی – Persian" lang="fa" hreflang="fa" data-title="کنترل تطبیقی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%81%EC%9D%91_%EC%A0%9C%EC%96%B4" title="적응 제어 – Korean" lang="ko" hreflang="ko" data-title="적응 제어" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%95%E0%A5%82%E0%A4%B2%E0%A5%80_%E0%A4%A8%E0%A4%BF%E0%A4%AF%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%A3" title="अनुकूली नियंत्रण – Hindi" lang="hi" hreflang="hi" data-title="अनुकूली नियंत्रण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Controllo_adattativo" title="Controllo adattativo – Italian" lang="it" hreflang="it" data-title="Controllo adattativo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Adaptieve_regeling" title="Adaptieve regeling – Dutch" lang="nl" hreflang="nl" data-title="Adaptieve regeling" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sterowanie_adaptacyjne" title="Sterowanie adaptacyjne – Polish" lang="pl" hreflang="pl" data-title="Sterowanie adaptacyjne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%B4%D0%B0%D0%BF%D1%82%D0%B8%D0%B2%D0%BD%D0%BE%D0%B5_%D1%83%D0%BF%D1%80%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Адаптивное управление – Russian" lang="ru" hreflang="ru" data-title="Адаптивное управление" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Adapt%C3%ADvne_riadenie" title="Adaptívne riadenie – Slovak" lang="sk" hreflang="sk" data-title="Adaptívne riadenie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Adaptiv_regulator" title="Adaptiv regulator – Swedish" lang="sv" hreflang="sv" data-title="Adaptiv regulator" data-language-autonym="Svenska" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Type of control method</div> <p><b>Adaptive control</b> is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.<sup id="cite_ref-Annaswamy_1-0" class="reference"><a href="#cite_note-Annaswamy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-CMP-AC-T-01_2-0" class="reference"><a href="#cite_note-CMP-AC-T-01-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions. Adaptive control is different from <a href="/wiki/Robust_control" title="Robust control">robust control</a> in that it does not need <i>a priori</i> information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is concerned with control law changing itself. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Parameter_estimation">Parameter estimation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=1" title="Edit section: Parameter estimation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The foundation of adaptive control is <a href="/wiki/Parameter_estimation" class="mw-redirect" title="Parameter estimation">parameter estimation</a>, which is a branch of <a href="/wiki/System_identification" title="System identification">system identification</a>. Common methods of estimation include <a href="/wiki/Recursive_least_squares" class="mw-redirect" title="Recursive least squares">recursive least squares</a> and <a href="/wiki/Gradient_descent" title="Gradient descent">gradient descent</a>. Both of these methods provide update laws that are used to modify estimates in real-time (i.e., as the system operates). <a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov stability</a> is used to derive these update laws and show convergence criteria (typically persistent excitation; relaxation of this condition are studied in Concurrent Learning adaptive control). <a href="/wiki/Projection_(mathematics)" title="Projection (mathematics)">Projection</a> and normalization are commonly used to improve the robustness of estimation algorithms. </p> <div class="mw-heading mw-heading2"><h2 id="Classification_of_adaptive_control_techniques">Classification of adaptive control techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=2" title="Edit section: Classification of adaptive control techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In general, one should distinguish between: </p> <ol><li>Feedforward adaptive control</li> <li>Feedback adaptive control</li></ol> <p>as well as between </p> <ol><li>Direct methods</li> <li>Indirect methods</li> <li>Hybrid methods</li></ol> <p>Direct methods are ones wherein the estimated parameters are those directly used in the adaptive controller. In contrast, indirect methods are those in which the estimated parameters are used to calculate required controller parameters.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Hybrid methods rely on both estimation of parameters and direct modification of the control law. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:MRAC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/MRAC.svg/320px-MRAC.svg.png" decoding="async" width="320" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/MRAC.svg/480px-MRAC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/MRAC.svg/640px-MRAC.svg.png 2x" data-file-width="585" data-file-height="232" /></a><figcaption>MRAC</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:MIAC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/MIAC.svg/320px-MIAC.svg.png" decoding="async" width="320" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/MIAC.svg/480px-MIAC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/MIAC.svg/640px-MIAC.svg.png 2x" data-file-width="585" data-file-height="232" /></a><figcaption>MIAC</figcaption></figure> <p>There are several broad categories of feedback adaptive control (classification can vary): </p> <ul><li>Dual adaptive controllers – based on <a href="/wiki/Dual_control_theory" title="Dual control theory">dual control theory</a> <ul><li>Optimal dual controllers – difficult to design</li> <li>Suboptimal dual controllers</li></ul></li> <li>Nondual adaptive controllers <ul><li>Adaptive pole placement</li> <li>Extremum-seeking controllers</li> <li><a href="/wiki/Iterative_learning_control" title="Iterative learning control">Iterative learning control</a></li> <li><a href="/wiki/Gain_scheduling" title="Gain scheduling">Gain scheduling</a></li> <li>Model reference adaptive controllers (MRACs) – incorporate a <i>reference model</i> defining desired closed <a href="/wiki/Loop_performance" title="Loop performance">loop performance</a> <ul><li>Gradient optimization MRACs – use local rule for adjusting params when performance differs from reference. Ex.: "MIT rule".</li> <li>Stability optimized MRACs</li></ul></li> <li>Model identification adaptive controllers (MIACs) – perform <a href="/wiki/System_identification" title="System identification">system identification</a> while the system is running <ul><li>Cautious adaptive controllers – use current SI to modify control law, allowing for SI uncertainty</li> <li>Certainty equivalent adaptive controllers – take current SI to be the true system, assume no uncertainty <ul><li>Nonparametric adaptive controllers</li> <li>Parametric adaptive controllers <ul><li>Explicit parameter adaptive controllers</li> <li>Implicit parameter adaptive controllers</li></ul></li></ul></li></ul></li> <li><a href="/wiki/Multiple_models" title="Multiple models">Multiple models</a> – Use large number of models, which are distributed in the region of uncertainty, and based on the responses of the plant and the models. One model is chosen at every instant, which is closest to the plant according to some metric.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:AdaptiveControl.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/AdaptiveControl.png/320px-AdaptiveControl.png" decoding="async" width="320" height="297" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/5a/AdaptiveControl.png 1.5x" data-file-width="438" data-file-height="407" /></a><figcaption>Adaptive control with Multiple Models</figcaption></figure> <p>Some special topics in adaptive control can be introduced as well: </p> <ol><li>Adaptive control based on discrete-time process identification</li> <li>Adaptive control based on the model reference control technique<sup id="cite_ref-Lavretsky_5-0" class="reference"><a href="#cite_note-Lavretsky-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li> <li>Adaptive control based on continuous-time process models</li> <li>Adaptive control of multivariable processes<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li>Adaptive control of nonlinear processes</li> <li>Concurrent learning adaptive control, which relaxes the condition on persistent excitation for parameter convergence for a class of systems<sup id="cite_ref-chowdhary1_7-0" class="reference"><a href="#cite_note-chowdhary1-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-chowdhary2_8-0" class="reference"><a href="#cite_note-chowdhary2-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li></ol> <p>In recent times, adaptive control has been merged with intelligent techniques such as fuzzy and neural networks to bring forth new concepts such as fuzzy adaptive control. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=3" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When designing adaptive control systems, special consideration is necessary of <a href="https://en.wiktionary.org/wiki/convergence" class="extiw" title="wikt:convergence">convergence</a> and <a href="/wiki/Robustness_(computer_science)" title="Robustness (computer science)">robustness</a> issues. Lyapunov stability is typically used to derive control adaptation laws and show . </p> <dl><dd></dd></dl> <ul><li>Self-tuning of subsequently fixed linear controllers during the implementation phase for one operating point;</li> <li>Self-tuning of subsequently fixed robust controllers during the implementation phase for whole range of operating points;</li> <li>Self-tuning of fixed controllers on request if the process behaviour changes due to ageing, drift, wear, etc.;</li> <li>Adaptive control of linear controllers for nonlinear or time-varying processes;</li> <li>Adaptive control or self-tuning control of nonlinear controllers for nonlinear processes;</li> <li>Adaptive control or self-tuning control of multivariable controllers for multivariable processes (MIMO systems);</li></ul> <p>Usually these methods adapt the controllers to both the process statics and dynamics. In special cases the adaptation can be limited to the static behavior alone, leading to adaptive control based on characteristic curves for the steady-states or to extremum value control, optimizing the steady state. Hence, there are several ways to apply adaptive control algorithms. </p><p>A particularly successful application of adaptive control has been adaptive flight control.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This body of work has focused on guaranteeing stability of a model reference adaptive control scheme using Lyapunov arguments. Several successful flight-test demonstrations have been conducted, including fault tolerant adaptive control.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Nonlinear_control" title="Nonlinear control">Nonlinear control</a></li> <li><a href="/wiki/Intelligent_control" title="Intelligent control">Intelligent control</a></li> <li><a href="/wiki/Lyapunov_optimization" title="Lyapunov optimization">Lyapunov optimization</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Annaswamy-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Annaswamy_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAnnaswamy2023" class="citation journal cs1">Annaswamy, Anuradha M. 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"Theory and flight-test validation of a concurrent learning adaptive controller". <i>Journal of Guidance, Control, and Dynamics</i>. <b>34</b> (2): 592–607. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011JGCD...34..592C">2011JGCD...34..592C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2514%2F1.46866">10.2514/1.46866</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Guidance%2C+Control%2C+and+Dynamics&rft.atitle=Theory+and+flight-test+validation+of+a+concurrent+learning+adaptive+controller&rft.volume=34&rft.issue=2&rft.pages=592-607&rft.date=2011&rft_id=info%3Adoi%2F10.2514%2F1.46866&rft_id=info%3Abibcode%2F2011JGCD...34..592C&rft.aulast=Chowdhary&rft.aufirst=Girish&rft.au=Johnson%2C+Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></span> </li> <li id="cite_note-chowdhary2-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-chowdhary2_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChowdharyMuehleggJohnson2014" class="citation journal cs1">Chowdhary, Girish; Muehlegg, Maximillian; Johnson, Eric (2014). "Exponential parameter and tracking error convergence guarantees for adaptive controllers without persistency of excitation". <i>International Journal of Control</i>. <b>87</b> (8): 1583–1603. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011JGCD...34..592C">2011JGCD...34..592C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2514%2F1.46866">10.2514/1.46866</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Control&rft.atitle=Exponential+parameter+and+tracking+error+convergence+guarantees+for+adaptive+controllers+without+persistency+of+excitation&rft.volume=87&rft.issue=8&rft.pages=1583-1603&rft.date=2014&rft_id=info%3Adoi%2F10.2514%2F1.46866&rft_id=info%3Abibcode%2F2011JGCD...34..592C&rft.aulast=Chowdhary&rft.aufirst=Girish&rft.au=Muehlegg%2C+Maximillian&rft.au=Johnson%2C+Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLavretsky2015" class="citation book cs1">Lavretsky, Eugene (2015). "Robust and Adaptive Control Methods for Aerial Vehicles". <i>Handbook of Unmanned Aerial Vehicles</i>. pp. 675–710. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-90-481-9707-1_50">10.1007/978-90-481-9707-1_50</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-9706-4" title="Special:BookSources/978-90-481-9706-4"><bdi>978-90-481-9706-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Robust+and+Adaptive+Control+Methods+for+Aerial+Vehicles&rft.btitle=Handbook+of+Unmanned+Aerial+Vehicles&rft.pages=675-710&rft.date=2015&rft_id=info%3Adoi%2F10.1007%2F978-90-481-9707-1_50&rft.isbn=978-90-481-9706-4&rft.aulast=Lavretsky&rft.aufirst=Eugene&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKannanChowdharyJohnson2015" class="citation book cs1">Kannan, Suresh K.; Chowdhary, Girish Vinayak; Johnson, Eric N. (2015). "Adaptive Control of Unmanned Aerial Vehicles: Theory and Flight Tests". <i>Handbook of Unmanned Aerial Vehicles</i>. pp. 613–673. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-90-481-9707-1_61">10.1007/978-90-481-9707-1_61</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-9706-4" title="Special:BookSources/978-90-481-9706-4"><bdi>978-90-481-9706-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Adaptive+Control+of+Unmanned+Aerial+Vehicles%3A+Theory+and+Flight+Tests&rft.btitle=Handbook+of+Unmanned+Aerial+Vehicles&rft.pages=613-673&rft.date=2015&rft_id=info%3Adoi%2F10.1007%2F978-90-481-9707-1_61&rft.isbn=978-90-481-9706-4&rft.aulast=Kannan&rft.aufirst=Suresh+K.&rft.au=Chowdhary%2C+Girish+Vinayak&rft.au=Johnson%2C+Eric+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChowdharyJohnsonChandramohanKimbrell2013" class="citation journal cs1">Chowdhary, Girish; Johnson, Eric N; Chandramohan, Rajeev; Kimbrell, Scott M; Calise, Anthony (2013). "Guidance and control of airplanes under actuator failures and severe structural damage". <i>Journal of Guidance, Control, and Dynamics</i>. <b>36</b> (4): 1093–1104. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013JGCD...36.1093C">2013JGCD...36.1093C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2514%2F1.58028">10.2514/1.58028</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Guidance%2C+Control%2C+and+Dynamics&rft.atitle=Guidance+and+control+of+airplanes+under+actuator+failures+and+severe+structural+damage&rft.volume=36&rft.issue=4&rft.pages=1093-1104&rft.date=2013&rft_id=info%3Adoi%2F10.2514%2F1.58028&rft_id=info%3Abibcode%2F2013JGCD...36.1093C&rft.aulast=Chowdhary&rft.aufirst=Girish&rft.au=Johnson%2C+Eric+N&rft.au=Chandramohan%2C+Rajeev&rft.au=Kimbrell%2C+Scott+M&rft.au=Calise%2C+Anthony&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=6" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>B. Egardt, Stability of Adaptive Controllers. New York: Springer-Verlag, 1979.</li> <li>I. D. Landau, Adaptive Control: The Model Reference Approach. New York: Marcel Dekker, 1979.</li> <li>P. A. Ioannou and J. Sun, Robust Adaptive Control. Upper Saddle River, NJ: Prentice-Hall, 1996.</li> <li>K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems. Englewood Cliffs, NJ: Prentice Hall, 1989; Dover Publications, 2004.</li> <li>S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness. Prentice Hall, 1989.</li> <li>K. J. Astrom and B. Wittenmark, Adaptive Control. Reading, MA: Addison-Wesley, 1995.</li> <li>I. D. Landau, R. Lozano, and M. M’Saad, Adaptive Control. New York, NY: Springer-Verlag, 1998.</li> <li>G. Tao, Adaptive Control Design and Analysis. Hoboken, NJ: Wiley-Interscience, 2003.</li> <li>P. A. Ioannou and B. Fidan, Adaptive Control Tutorial. SIAM, 2006.</li> <li>G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.</li> <li>M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. Wiley Interscience, 1995.</li> <li>P. A. Ioannou and P. V. Kokotovic, Adaptive Systems with Reduced Models. Springer Verlag, 1983.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnnaswamyFradkov2021" class="citation journal cs1">Annaswamy, Anuradha M.; Fradkov, Alexander L. (2021). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S1367578821000894">"A historical perspective of adaptive control and learning"</a>. <i>Annual Reviews in Control</i>. <b>52</b>: 18–41. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2108.11336">2108.11336</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.arcontrol.2021.10.014">10.1016/j.arcontrol.2021.10.014</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:237290042">237290042</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Reviews+in+Control&rft.atitle=A+historical+perspective+of+adaptive+control+and+learning&rft.volume=52&rft.pages=18-41&rft.date=2021&rft_id=info%3Aarxiv%2F2108.11336&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A237290042%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.arcontrol.2021.10.014&rft.aulast=Annaswamy&rft.aufirst=Anuradha+M.&rft.au=Fradkov%2C+Alexander+L.&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1367578821000894&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAdaptive+control" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Adaptive_control&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.ece.utah.edu/~bodson/acscr/">Shankar Sastry and Marc Bodson, Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, 1989-1994 (book)</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120218223836/http://www.pages.drexel.edu/~kws23/tutorials/MRAC/MRAC.html">K. Sevcik: Tutorial on Model Reference Adaptive Control (Drexel University)</a></li> <li><a rel="nofollow" class="external text" href="https://www.dropbox.com/sh/gnx898j6xl0x33r/AABKvpjX4HYi03S2efz9n32Ya?dl=0:">Tutorial on Concurrent Learning Model Reference Adaptive Control G. Chowdhary (slides, relevant papers, and matlab code)</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Adaptive_control&oldid=1251943195">https://en.wikipedia.org/w/index.php?title=Adaptive_control&oldid=1251943195</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Control_theory" title="Category:Control theory">Control theory</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">CS1 maint: multiple names: authors list</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 18 October 2024, at 23:33<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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