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By utilizing the finite-time stability theory, barrier Lyapunov functions and the adaptive backstepping method, a novel adaptive tracking control strategy is proposed. On the basis of the presented method, the finite-time control problem of the nonlinear system with dead-zone is solved. The finite-time controller is designed such that all the signals in the closed-loop system are bounded, the output is driven to track the reference signal to a small neighborhood and all states are ensured to remain in the predefined compact sets. Finally, the effectiveness of the proposed scheme is verified via some simulation results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7047059">Cited in <strong>141</strong> Documents</a></div></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%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%3A93B52" title="MSC2020">93B52</a> </td> <td class="space"> Feedback control </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%3Anonlinear+systems">nonlinear systems</a>; <a href="/?q=ut%3Aadaptive+finite-time+control">adaptive finite-time control</a>; <a href="/?q=ut%3Abarrier+Lyapunov+functions">barrier Lyapunov functions</a>; <a href="/?q=ut%3Adead-zone">dead-zone</a>; <a href="/?q=ut%3Afull+state+constraints">full state constraints</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 1411.93102" data-ciurl="/ci/07047059" data-biburl="/bibtex/07047059.bib" data-amsurl="/amsrefs/07047059.bib" data-xmlurl="/xml/07047059.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07047059.pdf" title="Zbl 1411.93102 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.automatica.2018.10.030" aria-label="DOI for “Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone”" title="10.1016/j.automatica.2018.10.030">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">Amato, F.; Ariola, M.; Dorato, P., Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica, 37, 9, 1459-1463 (2001) &middot; <a href="/0983.93060" class="nowrap">Zbl 0983.93060</a></td> </tr><tr> <td>[2]</td> <td class="space">Chen, M.; Ge, S. S.; Ren, B., Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints, Automatica, 47, 3, 452-465 (2011) &middot; <a href="/1219.93053" class="nowrap">Zbl 1219.93053</a></td> </tr><tr> <td>[3]</td> <td class="space">Du, H.; Li, S.; Qian, C., Finite-time attitude tracking control of spacecraft with application to attitude synchronization, IEEE Transactions on Automatic Control, 56, 11, 2711-2717 (2011) &middot; <a href="/1368.70036" class="nowrap">Zbl 1368.70036</a></td> </tr><tr> <td>[4]</td> <td class="space">Ge, S. S.; Hong, F.; Lee, T. H., Robust adaptive control of nonlinear systems with unknown time delays, Automatica, 41, 7, 1181-1190 (2005) &middot; <a href="/1078.93046" class="nowrap">Zbl 1078.93046</a></td> </tr><tr> <td>[5]</td> <td class="space">Ge, S. S.; Wang, C., Adaptive NN control of uncertain nonlinear pure-feedback systems, Automatica, 38, 4, 671-682 (2002) &middot; <a href="/0998.93025" class="nowrap">Zbl 0998.93025</a></td> </tr><tr> <td>[6]</td> <td class="space">He, W.; Chen, Y.; Yin, Z., Adaptive neural network control of an uncertain robot with full-state constraints, IEEE Transactions on Cybernetics, 46, 3, 620-629 (2016)</td> </tr><tr> <td>[7]</td> <td class="space">Hong, K. S., Asymptotic behavior analysis of a coupled time-varying system: application to adaptive systems, IEEE Transactions on Automatic Control, 42, 12, 1693-1697 (1997) &middot; <a href="/0900.93322" class="nowrap">Zbl 0900.93322</a></td> </tr><tr> <td>[8]</td> <td class="space">Hong, K. S.; Bentsman, J., Direct adaptive control of parabolic systems: Algorithm synthesis and convergence and stability analysis, IEEE Transactions on Automatic Control, 39, 10, 2018-2033 (1994) &middot; <a href="/0815.93049" class="nowrap">Zbl 0815.93049</a></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, 5, 858-862 (2006) &middot; <a href="/1366.93290" class="nowrap">Zbl 1366.93290</a></td> </tr><tr> <td>[10]</td> <td class="space">Hu, C.; Yao, B.; Chen, Z.; Wang, Q., Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks, IEEE Transactions on Control Systems Technology, 19, 6, 1559-1568 (2011)</td> </tr><tr> <td>[11]</td> <td class="space">Hu, C.; Yao, B.; Wang, Q., Adaptive robust precision motion control of systems with unknown input dead-zones: A case study with comparative experiments, IEEE Transactions on Industrial Electronics, 58, 6, 2454-2464 (2011)</td> </tr><tr> <td>[12]</td> <td class="space">Hu, C.; Yao, B.; Wang, Q., Performance-oriented adaptive robust control of a class of nonlinear systems preceded by unknown dead zone with comparative experimental results, IEEE/ASME Transactions on Mechatronics, 18, 1, 178-189 (2013)</td> </tr><tr> <td>[13]</td> <td class="space">Hua, C.; Liu, P. X.; Guan, X., Backstepping control for nonlinear systems with time delays and applications to chemical reactor systems, IEEE Transactions on Industrial Electronics, 56, 9, 3723-3732 (2009)</td> </tr><tr> <td>[14]</td> <td class="space">Huang, J.; Wen, C.; Wang, W.; Song, Y. D., Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications, Automatica, 69, 395-404 (2016) &middot; <a href="/1338.93186" class="nowrap">Zbl 1338.93186</a></td> </tr><tr> <td>[15]</td> <td class="space">Iqbal, M.; Rehan, M.; Hong, K. S.; Khaliq, A.; Rehman, S., Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation, Chaos, Solitons &amp; Fractals, 77, 158-169 (2015) &middot; <a href="/1353.34057" class="nowrap">Zbl 1353.34057</a></td> </tr><tr> <td>[16]</td> <td class="space">Kanellakopoulos, I.; Kokotovic, P. V.; Morse, A. S., Systematic design of adaptive controllers for feedback linearizable systems, (American control conference (1991)), 649-654</td> </tr><tr> <td>[17]</td> <td class="space">Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V., Adaptive nonlinear control without overparametrization, Systems &amp; Control Letters, 19, 3, 177-185 (1992) &middot; <a href="/0763.93043" class="nowrap">Zbl 0763.93043</a></td> </tr><tr> <td>[18]</td> <td class="space">Li, T.; Li, Z.; Wang, D.; Chen, C. L.P., Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions, IEEE Transactions on Neural Networks and Learning Systems, 26, 6, 1188-1201 (2015)</td> </tr><tr> <td>[19]</td> <td class="space">Li, Y.; Tong, S.; Li, T., Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones, IEEE Transactions on Fuzzy Systems, 23, 4, 1228-1241 (2015)</td> </tr><tr> <td>[20]</td> <td class="space">Liu, Y.; Lu, S.; Tong, S.; Chen, X.; Chen, C. L.P.; Li, D. J., Adaptive control-based Barrier Lyapunov Functions for a class of stochastic nonlinear systems with full state constraints, Automatica, 87, 83-93 (2018) &middot; <a href="/1378.93137" class="nowrap">Zbl 1378.93137</a></td> </tr><tr> <td>[21]</td> <td class="space">Liu, Y.; Tong, S., Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems, Automatica, 76, 143-152 (2017) &middot; <a href="/1352.93062" class="nowrap">Zbl 1352.93062</a></td> </tr><tr> <td>[22]</td> <td class="space">Ma, R.; Zhao, J., Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings, Automatica, 46, 11, 1819-1823 (2010) &middot; <a href="/1218.93075" class="nowrap">Zbl 1218.93075</a></td> </tr><tr> <td>[23]</td> <td class="space">Ngo, Q. H.; Hong, K. S., Adaptive sliding mode control of container cranes, IET Control Theory &amp; Applications, 6, 5, 662-668 (2012)</td> </tr><tr> <td>[24]</td> <td class="space">Qian, C.; Lin, W., Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization, Systems &amp; Control Letters, 42, 3, 185-200 (2001) &middot; <a href="/0974.93050" class="nowrap">Zbl 0974.93050</a></td> </tr><tr> <td>[25]</td> <td class="space">Tanaka, K.; Wang, H. O., Fuzzy control systems design and analysis: a linear matrix inequality approach (2004), John Wiley &amp; Sons</td> </tr><tr> <td>[26]</td> <td class="space">Tang, Z. L.; Ge, S. S.; Tee, K. P.; He, W., Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 46, 12, 1618-1629 (2016)</td> </tr><tr> <td>[27]</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, 4, 918-927 (2009) &middot; <a href="/1162.93346" class="nowrap">Zbl 1162.93346</a></td> </tr><tr> <td>[28]</td> <td class="space">Wang, F.; Chen, B.; Lin, C.; Zhang, J.; Meng, X., Adaptive neural network finite-time output feedback control of quantized nonlinear systems, IEEE Transactions on Cybernetics, 48, 6, 1839-1848 (2018)</td> </tr><tr> <td>[29]</td> <td class="space">Wang, F.; Chen, B.; Liu, X.; Lin, C., Finite-time adaptive fuzzy tracking control design for nonlinear systems, IEEE Transactions on Fuzzy Systems, 26, 3, 1207-1216 (2018)</td> </tr><tr> <td>[30]</td> <td class="space">Wang, L.; Li, H.; Zhou, Q.; Lu, R., Adaptive fuzzy control for nonstrict feedback systems with unmodeled dynamics and fuzzy dead zone via output feedback, IEEE Transactions on Cybernetics, 47, 9, 2400-2412 (2017)</td> </tr><tr> <td>[31]</td> <td class="space">Wen, G.; Chen, C. L.P.; Liu, Y.; Liu, Z., Neural network-based adaptive leader-following consensus control for a class of nonlinear multiagent state-delay systems, IEEE Transactions on Cybernetics, 47, 8, 2151-2160 (2017)</td> </tr><tr> <td>[32]</td> <td class="space">Wen, G.; Ge, S. S.; Tu, F.; Choo, Y. S., Artificial potential-based adaptive \(H_\infty\) synchronized tracking control for Accommodation Vessel, IEEE Transactions on Industrial Electronics, 64, 7, 5640-5647 (2017)</td> </tr><tr> <td>[33]</td> <td class="space">Wen, C.; Zhou, J.; Wang, W., Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions, Automatica, 45, 1, 55-67 (2009) &middot; <a href="/1154.93426" class="nowrap">Zbl 1154.93426</a></td> </tr><tr> <td>[34]</td> <td class="space">Yu, S.; Yu, X.; Shirinzadeh, B.; Man, Z., Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 41, 11, 1957-1964 (2005) &middot; <a href="/1125.93423" class="nowrap">Zbl 1125.93423</a></td> </tr><tr> <td>[35]</td> <td class="space">Zhang, H.; Yang, J.; Su, C. Y., T-S fuzzy-model-based robust \(H_\infty\) design for networked control systems with uncertainties, IEEE Transactions on Industrial Informatics, 3, 4, 289-301 (2007)</td> </tr><tr> <td>[36]</td> <td class="space">Zhu, Z.; Xia, Y.; Fu, M., Attitude stabilization of rigid spacecraft with finite-time convergence, International Journal of Robust and Nonlinear Control, 21, 6, 686-702 (2011) &middot; <a href="/1214.93100" class="nowrap">Zbl 1214.93100</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>

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