Document Zbl 1527.93310

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J. Robust Nonlinear Control</a> <a href="/?q=in%3A505235" title="Articles in this Issue">31, No. 14, 6934-6952 (2021)</a>. </div> <div class="abstract"><div class="pre">Summary: This paper considers an event-triggered adaptive fixed-time output feedback fault tolerant control problem for a class of uncertain planar nonlinear systems, in which the actuator has an unknown drift fault and the loss of effectiveness fault. Firstly, by using the adaptive backstepping technique and event-triggered theory, a constructive event-triggered adaptive fixed-time state feedback controller is presented under a generalized Lipschitz continuous condition. Secondly, for the unmeasured state, a continuous fixed-time observer is constructed. It is shown that the global practically fixed-time stability of the closed-loop systems is ensured by the bilimit homogeneity technique and Lyapunov theory analysis. Moreover, the system is demonstrated by contradiction to be nonzeno. Finally, the fan speed control system is constructed to demonstrate the validity of the proposed strategy and the application of the general systems.<br class="zbmathjax-paragraph">{© 2021 John Wiley & Sons Ltd.}</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7769478">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C65" title="MSC2020">93C65</a> </td> <td class="space"> Discrete event control/observation systems </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%3A93D40" title="MSC2020">93D40</a> </td> <td class="space"> Finite-time stability </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </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%3A93C73" title="MSC2020">93C73</a> </td> <td class="space"> Perturbations in control/observation systems </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%3Aevent-triggered+adaptive+control">event-triggered adaptive control</a>; <a href="/?q=ut%3Afault+tolerant+control">fault tolerant control</a>; <a href="/?q=ut%3Afixed-time+stabilization">fixed-time stabilization</a>; <a href="/?q=ut%3Aoutput+feedback">output feedback</a>; <a href="/?q=ut%3Aplanar+nonlinear+systems">planar nonlinear systems</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 1527.93310" data-ciurl="/ci/07769478" data-biburl="/bibtex/07769478.bib" data-amsurl="/amsrefs/07769478.bib" data-xmlurl="/xml/07769478.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07769478.pdf" title="Zbl 1527.93310 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/10.1002/rnc.5655" aria-label="DOI for “Event-triggered adaptive fixed-time output feedback fault tolerant control for perturbed planar nonlinear systems”" title="10.1002/rnc.5655">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">Zhang, Y.; Jiang, J., Bibliographical review on reconfigurable fault‐tolerant control systems, Annu Rev Control, 32, 2, 229-252, 2008</td> </tr><tr> <td>[2]</td> <td class="space">Yu, X.; Jiang, J., A survey of fault‐tolerant controllers based on safety‐related issues, Annu Rev Control, 39, 46-57, 2015</td> </tr><tr> <td>[3]</td> <td class="space">Zhu, C.; Li, C.; Zhang, K.; Wei, H., 2017</td> </tr><tr> <td>[4]</td> <td class="space">Yu, X.; Fu, Y.; Li, P.; Zhang, Y., Fault‐tolerant aircraft control based on self‐constructing fuzzy neural networks and multivariable SMC under actuator faults, IEEE Trans Fuzzy Syst, 26, 4, 2324-2335, 2017</td> </tr><tr> <td>[5]</td> <td class="space">Zou, W.; Ahn, CK; Xiang, Z., Analysis on existence of compact set in neural network control for nonlinear systems, Automatica, 120, 109155, 2020 · <a href="/1448.93126" class="nowrap">Zbl 1448.93126</a></td> </tr><tr> <td>[6]</td> <td class="space">Zhu, C.; Li, C.; Chen, X.; Zhang, K.; Xin, X.; Wei, H., Event‐triggered adaptive fault tolerant control for a class of uncertain nonlinear systems, Entropy, 22, 6, 598, 2020</td> </tr><tr> <td>[7]</td> <td class="space">Yu, X.; Liu, Z.; Zhang, Y., Fault‐tolerant formation control of multiple UAVs in the presence of actuator faults, Int J Robust Nonlinear Control, 26, 12, 2668-2685, 2016 · <a href="/1346.93046" class="nowrap">Zbl 1346.93046</a></td> </tr><tr> <td>[8]</td> <td class="space">Pang, G.; Cao, J.; Chen, X.; Qiu, J., Simultaneous fault detection and antisaturated control based on dynamic observer for inverted pendulum control system, Int J Robust Nonlinear Control, 29, 11, 3279-3295, 2019 · <a href="/1426.93324" class="nowrap">Zbl 1426.93324</a></td> </tr><tr> <td>[9]</td> <td class="space">Hosseinzadeh, M.; Salmasi, FR, Fault‐tolerant supervisory controller for a hybrid AC/DC micro‐grid, IEEE Trans Smart Grid, 9, 4, 2809-2823, 2016</td> </tr><tr> <td>[10]</td> <td class="space">Yan, K.; Chen, M.; Wu, Q.; Jiang, B., Extended state observer‐based sliding mode fault‐tolerant control for unmanned autonomous helicopter with wind gusts, IET Control Theory Appl, 13, 10, 1500-1513, 2019 · <a href="/1432.93240" class="nowrap">Zbl 1432.93240</a></td> </tr><tr> <td>[11]</td> <td class="space">Sun, ZY; Peng, Y.; Wen, C.; Meng, Q., Fast finite‐time adaptive stabilization of high‐order uncertain nonlinear system with an asymmetric output constraint, Automatica, 121, 109170, 2020 · <a href="/1448.93287" class="nowrap">Zbl 1448.93287</a></td> </tr><tr> <td>[12]</td> <td class="space">Fang, L.; Ma, L.; Ding, S.; Zhao, D., Robust finite‐time stabilization of a class of high‐order stochastic nonlinear systems subject to output constraint and disturbances, Int J Robust Nonlinear Control, 29, 16, 5550-5573, 2019 · <a href="/1430.93173" class="nowrap">Zbl 1430.93173</a></td> </tr><tr> <td>[13]</td> <td class="space">Ding, S.; Park, JH; Chen, CC, Second‐order sliding mode controller design with output constraint, Automatica, 112, 108704, 2020 · <a href="/1430.93028" class="nowrap">Zbl 1430.93028</a></td> </tr><tr> <td>[14]</td> <td class="space">Li, S.; Du, H.; Lin, X., Finite‐time consensus algorithm for multi‐agent systems with double‐integrator dynamics, Automatica, 47, 8, 1706-1712, 2011 · <a href="/1226.93014" class="nowrap">Zbl 1226.93014</a></td> </tr><tr> <td>[15]</td> <td class="space">Jin, X., Fault tolerant finite‐time leader‐follower formation control for autonomous surface vessels with LOS range and angle constraints, Automatica, 68, 68, 228-236, 2016 · <a href="/1334.93007" class="nowrap">Zbl 1334.93007</a></td> </tr><tr> <td>[16]</td> <td class="space">Yu, X.; Liu, Z.; Zhang, Y., Fault‐tolerant flight control design with finite‐time adaptation under actuator stuck failures, IEEE Trans Control Syst Technol, 25, 4, 1431-1440, 2016</td> </tr><tr> <td>[17]</td> <td class="space">Van, M.; Ge, SS; Ren, H., Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control, IEEE Trans Syst Man Cybern, 47, 7, 1681-1693, 2017</td> </tr><tr> <td>[18]</td> <td class="space">Liu, L.; Liu, Y.; Tong, S., Neural networks‐based adaptive finite‐time fault‐tolerant control for a class of strict‐feedback switched nonlinear systems, IEEE Trans Syst Man Cybern, 49, 7, 2536-2545, 2019</td> </tr><tr> <td>[19]</td> <td class="space">Yu, X.; Li, P.; Zhang, Y., The design of fixed‐time observer and finite‐time fault‐tolerant control for hypersonic gliding vehicles, IEEE Trans Ind Electron, 65, 5, 4135-4144, 2017</td> </tr><tr> <td>[20]</td> <td class="space">Andrieu, V.; Praly, L.; Astolfi, A., Homogeneous approximation, recursive observer design, and output feedback, SIAM J Control Optim, 47, 4, 1814-1850, 2008 · <a href="/1165.93020" class="nowrap">Zbl 1165.93020</a></td> </tr><tr> <td>[21]</td> <td class="space">Polyakov, A., Nonlinear feedback design for fixed‐time stabilization of linear control systems, IEEE Trans Autom Control, 57, 8, 2106-2110, 2012 · <a href="/1369.93128" class="nowrap">Zbl 1369.93128</a></td> </tr><tr> <td>[22]</td> <td class="space">Sun, H.; Hou, L.; Zong, G.; Yu, X., Fixed‐time attitude tracking control for spacecraft with input quantization, IEEE Trans Aerosp Electron Syst, 55, 1, 124-134, 2018</td> </tr><tr> <td>[23]</td> <td class="space">Sun, H.; Hou, L.; Li, C., Synchronization of single‐degree‐of‐freedom oscillators via neural network based on fixed‐time terminal sliding mode control scheme, Neural Comput Appl, 31, 10, 6365-6372, 2019</td> </tr><tr> <td>[24]</td> <td class="space">Ding, S.; Levant, A.; Li, S., Simple homogeneous sliding‐mode controller, Automatica, 67, 22-32, 2016 · <a href="/1335.93032" class="nowrap">Zbl 1335.93032</a></td> </tr><tr> <td>[25]</td> <td class="space">Zuo, Z., Nonsingular fixed‐time consensus tracking for second‐order multi‐agent networks, Automatica, 54, 54, 305-309, 2015 · <a href="/1318.93010" class="nowrap">Zbl 1318.93010</a></td> </tr><tr> <td>[26]</td> <td class="space">Zhang, Z.; Wu, Y., Fixed‐time regulation control of uncertain nonholonomic systems and its applications, Int J Control, 90, 7, 1327-1344, 2017 · <a href="/1367.93595" class="nowrap">Zbl 1367.93595</a></td> </tr><tr> <td>[27]</td> <td class="space">Yu, X.; Li, P.; Zhang, Y., Fixed‐time actuator fault accommodation applied to hypersonic gliding vehicles, IEEE Trans Autom Sci Eng, 2020 · <a href="https://doi.org/10.1109/TASE.2020.3008846" class="nowrap">doi:10.1109/TASE.2020.3008846</a></td> </tr><tr> <td>[28]</td> <td class="space">Zhang, L.; Wei, C.; Wu, R.; Cui, N., Fixed‐time extended state observer based non‐singular fast terminal sliding mode control for a VTVL reusable launch vehicle, Aerosp Sci Technol, 82, 70-79, 2018</td> </tr><tr> <td>[29]</td> <td class="space">Zhang, J.; Yu, S.; Yan, Y., Fixed‐time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties, ISA Trans, 93, 145-155, 2019</td> </tr><tr> <td>[30]</td> <td class="space">Yin, Z.; Luo, J.; Wei, C., Quasi fixed‐time fault‐tolerant control for nonlinear mechanical systems with enhanced performance, Appl Math Comput, 352, 157-173, 2019 · <a href="/1428.70046" class="nowrap">Zbl 1428.70046</a></td> </tr><tr> <td>[31]</td> <td class="space">Li, S.; Guo, J.; Xiang, Z., Global stabilization of a class of switched nonlinear systems under sampled‐data control, IEEE Trans Syst Man Cybern Syst, 49, 9, 1912-1919, 2018</td> </tr><tr> <td>[32]</td> <td class="space">Li, S.; Ahn, CK; Guo, J.; Xiang, Z., Global output feedback sampled‐data stabilization of a class of switched nonlinear systems in the p‐normal form, IEEE Trans Syst Man Cybern Syst, 51, 2, 1075-1084, 2021</td> </tr><tr> <td>[33]</td> <td class="space">Zong, G.; Ren, H., Guaranteed cost finite‐time control for semi‐Markov jump systems with event‐triggered scheme and quantization input, Int J Robust Nonlinear Control, 29, 15, 5251-5273, 2019 · <a href="/1426.93316" class="nowrap">Zbl 1426.93316</a></td> </tr><tr> <td>[34]</td> <td class="space">Liu, T.; Jiang, ZP, Event‐based control of nonlinear systems with partial state and output feedback, Automatica, 53, 10-22, 2015 · <a href="/1371.93128" class="nowrap">Zbl 1371.93128</a></td> </tr><tr> <td>[35]</td> <td class="space">Zhang, C.; Yang, G., Event‐triggered practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems, Int J Robust Nonlinear Control, 29, 10, 3078-3092, 2019 · <a href="/1418.93227" class="nowrap">Zbl 1418.93227</a></td> </tr><tr> <td>[36]</td> <td class="space">Sun, W.; Zhao, J.; Sun, W.; Xia, J.; Sun, ZY, Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems, Int J Robust Nonlinear Control, 30, 9, 3773-3785, 2020 · <a href="/1466.93091" class="nowrap">Zbl 1466.93091</a></td> </tr><tr> <td>[37]</td> <td class="space">Zong, G.; Ren, H.; Karimi, HR, Event‐triggered communication and annular finite‐time $H_{\operatorname{\infty}}$ filtering for networked switched systems, IEEE Trans Cybern, 2020 · <a href="https://doi.org/10.1109/TCYB.2020.3010917" class="nowrap">doi:10.1109/TCYB.2020.3010917</a></td> </tr><tr> <td>[38]</td> <td class="space">Sun, ZY; Zhou, C.; Liu, ZG; Meng, Q., Fast finite‐time adaptive event‐triggered tracking for uncertain nonlinear systems, Int J Robust Nonlinear Control, 2020 · <a href="/1525.93393" class="nowrap">Zbl 1525.93393</a> · <a href="https://doi.org/10.1002/rnc.5196" class="nowrap">doi:10.1002/rnc.5196</a></td> </tr><tr> <td>[39]</td> <td class="space">Tian, B.; Zuo, Z.; Yan, X.; Wang, H., A fixed‐time output feedback control scheme for double integrator systems, Automatica, 80, 80, 17-24, 2017 · <a href="/1370.93202" class="nowrap">Zbl 1370.93202</a></td> </tr><tr> <td>[40]</td> <td class="space">Su, Y.; Zheng, C., Global fixed‐time output feedback stabilization for a class of double integrator systems, IEEE Trans Circuits Syst II Express Briefs, 67, 10, 1954-1958, 2020</td> </tr><tr> <td>[41]</td> <td class="space">Gao, F.; Zhu, C.; Huang, J.; Wu, Y., Global fixed‐time output feedback stabilization of perturbed planar nonlinear systems, IEEE Trans Circuits Syst II Express Briefs, 2020 · <a href="https://doi.org/10.1109/TCSII.2020.3006195" class="nowrap">doi:10.1109/TCSII.2020.3006195</a></td> </tr><tr> <td>[42]</td> <td class="space">Wu, K.; Yu, J.; Sun, C., Global robust regulation control for a class of cascade nonlinear systems subject to external disturbance, Nonlinear Dyn, 90, 2, 1209-1222, 2017 · <a href="/1390.93272" class="nowrap">Zbl 1390.93272</a></td> </tr><tr> <td>[43]</td> <td class="space">Su, Y.; Zheng, C., Robust finite‐time output feedback control of perturbed double integrator, Automatica, 60, 86-91, 2015 · <a href="/1331.93177" class="nowrap">Zbl 1331.93177</a></td> </tr><tr> <td>[44]</td> <td class="space">Hong, Y.; Wang, K.; Xi, Z., Stabilization of uncertain chained form systems within finite settling time, IEEE Trans Autom Control, 50, 9, 1379-1384, 2005 · <a href="/1365.93444" class="nowrap">Zbl 1365.93444</a></td> </tr><tr> <td>[45]</td> <td class="space">Khalil, HK; Grizzle, JW, Nonlinear Systems, 2002, Upper Saddle River, NJ: Prentice Hall · <a href="/1003.34002" class="nowrap">Zbl 1003.34002</a></td> </tr><tr> <td>[46]</td> <td class="space">Sun, ZY; Shao, Y.; Chen, CC, Fast finite‐time stability and its application in adaptive control of high‐order nonlinear system, Automatica, 106, 339-348, 2019 · <a href="/1429.93323" class="nowrap">Zbl 1429.93323</a></td> </tr><tr> <td>[47]</td> <td class="space">Chesi, G.; Garulli, A.; Tesi, A.; Vicino, A., Homogeneous Lyapunov functions for systems with structured uncertainties, Automatica, 39, 6, 1027-1035, 2003 · <a href="/1079.93036" class="nowrap">Zbl 1079.93036</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 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"> © 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 & 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=20250307"></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"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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