Document Zbl 1536.93487

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Sci.</a> <a href="/?q=in%3A510839" title="Articles in this Issue">661, Article ID 120148, 23 p. (2024)</a>. </div> <div class="abstract">Summary: To solve the problem that the controlled object and system model cannot be fully mastered or the system parameters cannot be well obtained through conventional measurement methods, in this paper, a novel adaptive fuzzy finite-time PID backstepping control method is developed for a class of nonlinear chaotic systems with full state constraints and unmodeled dynamics. The unmodeled dynamics are handled by employing a dynamic signal. To avoid the violations of full state constraints (FSCs), a barrier Lyapunov function is used to implement a PID backstepping framework, whose merit consists in that three control gain constants $K^P$, $K^I$ and $K^D$ with corresponding proportional relationships are designed to further improve control precision. Besides, the PID control method also embodies three dynamic gain components $\Delta K^P$, $\Delta K^I$ and $\Delta K^D$, all of which are free functions that can be self-tuning online, and have a significant link with the adaptive law and modify accordingly. Finally, theoretical analysis confirms that all signals are ultimately uniformly bounded, the error signal converges to a nearby area near the origin in a finite-time, and the FSCs are not smashed. The practicality of the proposed method is confirmed by two simulation studies using the second-order Duffing chaotic system and third-order Chua’s circuit.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A93C42" title="MSC2020">93C42</a> </td> <td class="space"> Fuzzy control/observation systems </td> </tr><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%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aadaptive+fuzzy+control">adaptive fuzzy control</a>; <a href="/?q=ut%3Afinite-time+control">finite-time control</a>; <a href="/?q=ut%3APID+backstepping+control">PID backstepping control</a>; <a href="/?q=ut%3Achaotic+system">chaotic system</a>; <a href="/?q=ut%3Afull+states+constraint">full states constraint</a></div>  <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">×</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;">  </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">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1536.93487" data-ciurl="/ci/07829839" data-biburl="/bibtex/07829839.bib" data-amsurl="/amsrefs/07829839.bib" data-xmlurl="/xml/07829839.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07829839.pdf" title="Zbl 1536.93487 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.2024.120148" aria-label="DOI for “Adaptive fuzzy finite-time PID backstepping control for chaotic systems with full states constraints and unmodeled dynamics”" title="10.1016/j.ins.2024.120148">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">Hua, C.; Guan, X., Adaptive control for chaotic systems, Chaos Solitons Fractals, 22, 1, 55-60 (2004) · <a href="/1069.93016" class="nowrap">Zbl 1069.93016</a></td> </tr><tr> <td>[2]</td> <td class="space">Konishi, K.; Hirai, M.; Kokame, H., Sliding mode control for a class of chaotic systems, Phys. 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