Document Zbl 1534.93221

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J. Robust Nonlinear Control</a> <a href="/?q=in%3A509736" title="Articles in this Issue">33, No. 15, 9251-9270 (2023)</a>. </div> <div class="abstract">Summary: The adaptive technique and sliding-mode algorithm (SMA) for observer-based fault tolerant control is discussed with dynamic event-triggered scheme (DETS) in this article. Both the actuator and communication faults are considered, which implies that the inputs of system and controller are unreliable. Moreover, the switched DETS for controller-actuator channel is proposed to reduce bandwidth usage and actuator action frequency, which is different from the traditional event-triggered strategies. To deal with communication faults, which can be described as packet losses, the closed-loop system is modeled as a stochastic system. The SMA-based observer is designed to estimate system states, which lays the foundation for the design of control algorithm to mitigate the effects of faults and DETS. Then, a novel observer-based adaptive sliding-mode control (SMC) law based on hyperbolic tangent function is proposed to guarantee the stochastic globally uniformly ultimately boundedness and reduce chattering. At last, the proposed DETS and observer-based adaptive SMC law are applied into a robotic arm to illustrate the validity.<br class="zbmathjax-paragraph">© 2022 John Wiley & Sons Ltd.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7816538">Cited in <strong>5</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%3A93B12" title="MSC2020">93B12</a> </td> <td class="space"> Variable structure systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B53" title="MSC2020">93B53</a> </td> <td class="space"> Observers </td> </tr><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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aactuator+and+communication+faults">actuator and communication faults</a>; <a href="/?q=ut%3Adynamic+event-triggered+scheme">dynamic event-triggered scheme</a>; <a href="/?q=ut%3Aobserver-based+adaptive+SMC">observer-based adaptive SMC</a>; <a href="/?q=ut%3Astochastic+system">stochastic system</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 1534.93221" data-ciurl="/ci/07816538" data-biburl="/bibtex/07816538.bib" data-amsurl="/amsrefs/07816538.bib" data-xmlurl="/xml/07816538.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07816538.pdf" title="Zbl 1534.93221 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.6320" aria-label="DOI for “Observer-based adaptive sliding-mode control under dynamic event-triggered scheme with actuator and communication faults”" title="10.1002/rnc.6320">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">Ríos, H.; Falcón, R.; González, OA; Dzul, A., Continuous sliding‐mode control strategies for quadrotor robust tracking: real‐time application, IEEE Trans Ind Electron, 66, 2, 1264-1272, 2018</td> </tr><tr> <td>[2]</td> <td class="space">Henry, D.; Zenteno‐Torres, J.; Cieslak, J.; De Loza, AF; Dávila, J., A 6‐DOF sliding mode fault tolerant control solution for in‐orbit autonomous rendezvous, Aerosp Sci Technol, 2021</td> </tr><tr> <td>[3]</td> <td class="space">Fei, J.; Chen, Y., Dynamic terminal sliding‐mode control for single‐phase active power filter using new feedback recurrent neural network, IEEE Trans Power Electron, 35, 9, 9904-9922, 2020</td> </tr><tr> <td>[4]</td> <td class="space">Qi, W.; Zong, G.; Karim, HR, Observer‐based adaptive SMC for nonlinear uncertain singular semi‐Markov jump systems with applications to DC motor, IEEE Trans Circuits Syst I Regul Pap, 65, 9, 2951-2960, 2018 · <a href="/1468.93159" class="nowrap">Zbl 1468.93159</a></td> </tr><tr> <td>[5]</td> <td class="space">Wang, J.; Zhao, Y.; Bao, Y.; Kim, HH; Min, CL, Trajectory tracking control using fractional‐order terminal sliding mode control with sliding perturbation observer for a 7‐DOF robot manipulator, IEEE/ASME Trans Mechatron, 99, 1, 2020</td> </tr><tr> <td>[6]</td> <td class="space">Herrera, M.; Camacho, O.; Leiva, H.; Smith, C., An approach of dynamic sliding mode control for chemical processes, J Process Control, 85, 112-120, 2020</td> </tr><tr> <td>[7]</td> <td class="space">Liu, X.; Su, X.; Shi, P.; Shen, C.; Peng, Y., Event‐triggered sliding mode control of nonlinear dynamic systems, Automatica, 112, 2020 · <a href="/1430.93029" class="nowrap">Zbl 1430.93029</a></td> </tr><tr> <td>[8]</td> <td class="space">Liu, YA; Tang, S.; Liu, Y.; Kong, Q.; Wang, J., Extended dissipative sliding mode control for nonlinear networked control systems via event‐triggered mechanism with random uncertain measurement, Appl Math Comput, 396, 2021 · <a href="/1508.93306" class="nowrap">Zbl 1508.93306</a></td> </tr><tr> <td>[9]</td> <td class="space">Roy, S.; Baldi, S.; Fridman, LM, On adaptive sliding mode control without a priori bounded uncertainty, Automatica, 111, 2020 · <a href="/1430.93031" class="nowrap">Zbl 1430.93031</a></td> </tr><tr> <td>[10]</td> <td class="space">Zhang, L.; Guo, G., Observer‐based adaptive event‐triggered sliding mode control of saturated nonlinear networked systems with cyber‐attacks, Inf Sci, 543, 180-201, 2021 · <a href="/1478.93431" class="nowrap">Zbl 1478.93431</a></td> </tr><tr> <td>[11]</td> <td class="space">Zhang, D.; Wang, QG; Feng, G.; Shi, Y.; Vasilakos, AV, A survey on attack detection, estimation and control of industrial cyber-physical systems, ISA Trans, 116, 1-16, 2021</td> </tr><tr> <td>[12]</td> <td class="space">Xiong, J.; Chang, XH; Park, JH; Li, ZM, Nonfragile fault‐tolerant control of suspension systems subject to input quantization and actuator fault, Int J Robust Nonlinear Control, 30, 16, 6720-6743, 2020 · <a href="/1525.93058" class="nowrap">Zbl 1525.93058</a></td> </tr><tr> <td>[13]</td> <td class="space">Franco, R.; Ríos, H.; de Loza, AF; Efimov, D., A robust nonlinear model reference adaptive control for disturbed linear systems: an LMI approach, IEEE Trans Automat Contr, 67, 4, 1937-1943, 2021 · <a href="/1537.93385" class="nowrap">Zbl 1537.93385</a></td> </tr><tr> <td>[14]</td> <td class="space">Sun, K.; Liu, L.; Qiu, J.; Feng, G., Fuzzy adaptive finite‐time fault‐tolerant control for strict‐feedback nonlinear systems, IEEE Trans Fuzzy Syst, 29, 4, 786-796, 2020</td> </tr><tr> <td>[15]</td> <td class="space">Wang, Y.; Xu, N.; Liu, Y.; Zhao, X., Adaptive fault‐tolerant control for switched nonlinear systems based on command filter technique, Appl Math Comput, 392, 2021 · <a href="/1508.93180" class="nowrap">Zbl 1508.93180</a></td> </tr><tr> <td>[16]</td> <td class="space">Ma, L.; Xu, N.; Zhao, X.; Zong, G.; Huo, X., Small‐gain technique‐based adaptive neural output‐feedback fault‐tolerant control of switched nonlinear systems with unmodeled dynamics, IEEE Trans Syst Man Cybern Syst, 51, 11, 7051-7062, 2020</td> </tr><tr> <td>[17]</td> <td class="space">Zhu, JW; Gu, CY; Ding, SX; Zhang, WA; Wang, X.; Yu, L., A new observer‐based cooperative fault‐tolerant tracking control method with application to networked multiaxis motion control system, IEEE Trans Ind Electron, 68, 8, 7422-7432, 2020</td> </tr><tr> <td>[18]</td> <td class="space">Zhu, C.; Zhang, K.; Xin, X.; Gao, F.; Wei, H., Event‐triggered adaptive fixed‐time output feedback fault tolerant control for perturbed planar nonlinear systems, Int J Robust Nonlinear Control, 31, 14, 6934-6952, 2021 · <a href="/1527.93310" class="nowrap">Zbl 1527.93310</a></td> </tr><tr> <td>[19]</td> <td class="space">Chen, L.; Edwards, C.; Alwi, H.; Sato, M., Flight evaluation of a sliding mode online control allocation scheme for fault tolerant control, Automatica, 114, 2020 · <a href="/1441.93047" class="nowrap">Zbl 1441.93047</a></td> </tr><tr> <td>[20]</td> <td class="space">Ijaz, S.; Chen, F.; Tariq, HM, A new actuator fault‐tolerant control for Lipschitz nonlinear system using adaptive sliding mode control strategy, Int J Robust Nonlinear Control, 31, 6, 2305-2333, 2021 · <a href="/1526.93036" class="nowrap">Zbl 1526.93036</a></td> </tr><tr> <td>[21]</td> <td class="space">Van, M.; Ge, SS, Adaptive fuzzy integral sliding‐mode control for robust fault‐tolerant control of robot manipulators with disturbance observer, IEEE Trans Fuzzy Syst, 29, 5, 1284-1296, 2020</td> </tr><tr> <td>[22]</td> <td class="space">Wang, J.; Fang, F.; Yi, X.; Liu, Y., Dynamic event‐triggered fault estimation and sliding mode fault‐tolerant control for networked control systems with sensor faults, Appl Math Comput, 389, 2021 · <a href="/1508.93213" class="nowrap">Zbl 1508.93213</a></td> </tr><tr> <td>[23]</td> <td class="space">Wang, G.; Hao, X.; Zhao, N.; Zhang, G.; Xu, D., Current sensor fault‐tolerant control strategy for encoderless PMSM drives based on single sliding mode observer, IEEE Trans Transp Electrif, 6, 2, 679-689, 2020</td> </tr><tr> <td>[24]</td> <td class="space">Hu, JW; Zhan, XS; Wu, J.; Yan, HC, Analysis of optimal performance of MIMO networked control systems with encoding and packet dropout constraints, IET Control Theory Appl, 14, 13, 1762-1768, 2020 · <a href="/1542.93198" class="nowrap">Zbl 1542.93198</a></td> </tr><tr> <td>[25]</td> <td class="space">Wang, X.; Park, JH; Liu, H.; Zhang, X., Cooperative output‐feedback secure control of distributed linear cyber‐physical systems resist intermittent dos attacks, IEEE Trans Cybern, 51, 10, 4924-4933, 2020</td> </tr><tr> <td>[26]</td> <td class="space">Chen, Y.; Zhang, D.; Zhang, H.; Wang, QG, Dual‐path mixed domain residual threshold networks for bearing fault diagnosis, IEEE Trans Ind Electron, 2022</td> </tr><tr> <td>[27]</td> <td class="space">Xiao, G.; Liu, F., Observer‐based cooperative distributed fault‐tolerant model predictive control with imperfect network communication and asynchronous measurements, Int J Robust Nonlinear Control, 30, 12, 4531-4549, 2020 · <a href="/1466.93049" class="nowrap">Zbl 1466.93049</a></td> </tr><tr> <td>[28]</td> <td class="space">Su, X.; Wang, C.; Chang, H.; Yang, Y.; Assawinchaichote, W., Event‐triggered sliding mode control of networked control systems with Markovian jump parameters, Automatica, 125, 2021 · <a href="/1461.93318" class="nowrap">Zbl 1461.93318</a></td> </tr><tr> <td>[29]</td> <td class="space">Yu, Z.; Yu, S.; Jiang, H.; Hu, C., Distributed consensus for multi‐agent systems via adaptive sliding mode control, Int J Robust Nonlinear Control, 2021</td> </tr><tr> <td>[30]</td> <td class="space">Kumari, K.; Bandyopadhyay, B.; Reger, J.; Behera, AK, Event‐triggered sliding mode control for a high‐order system via reduced‐order model based design, Automatica, 121, 2020 · <a href="/1448.93197" class="nowrap">Zbl 1448.93197</a></td> </tr><tr> <td>[31]</td> <td class="space">Liu, J.; Yin, T.; Cao, J.; Yue, D.; Karimi, HR, Security control for T-S fuzzy systems with adaptive event‐triggered mechanism and multiple cyber‐attacks, IEEE Trans Syst Man Cybern Syst, 51, 10, 6544-6554, 2020</td> </tr><tr> <td>[32]</td> <td class="space">Li, W.; Xie, Z.; Zhao, J.; Wong, PK, Velocity‐based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication, Mech Syst Signal Process, 143, 2020</td> </tr><tr> <td>[33]</td> <td class="space">Long, ZA; Ge, G., Observer‐based adaptive event‐triggered sliding mode control of saturated nonlinear networked systems with cyber‐attacks ‐ ScienceDirect, Inf Sci, 543, 180-201, 2021 · <a href="/1478.93431" class="nowrap">Zbl 1478.93431</a></td> </tr><tr> <td>[34]</td> <td class="space">Ye, Z.; Zhang, D.; Wu, ZG; Yan, H., A3c‐based intelligent event‐triggering control of networked nonlinear unmanned marine vehicles subject to hybrid attacks, IEEE Trans Intell Transp Syst, 2021</td> </tr><tr> <td>[35]</td> <td class="space">Cheng, J.; Wu, Y.; Yan, H.; Wu, ZG; Shi, K., Protocol‐based filtering for fuzzy Markov affine systems with switching chain, Automatica, 141, 2022 · <a href="/1491.93121" class="nowrap">Zbl 1491.93121</a></td> </tr><tr> <td>[36]</td> <td class="space">Cheng, J.; Xie, L.; Park, JH; Yan, H., Protocol‐based output‐feedback control for Semi‐Markov jump systems, IEEE Trans Automat Contr, 2022 · <a href="/1537.93238" class="nowrap">Zbl 1537.93238</a></td> </tr><tr> <td>[37]</td> <td class="space">Cao, Z.; Niu, Y.; Lam, HK; Zhao, J., Sliding mode control of Markovian jump fuzzy systems: a dynamic event‐triggered method, IEEE Trans Fuzzy Syst, 29, 10, 2902-2915, 2020</td> </tr><tr> <td>[38]</td> <td class="space">Yesmin, A.; Behera, AK; Bera, MK; Bandyopadhyay, B., Dynamic event‐triggering based design of sliding mode control, Int J Robust Nonlinear Control, 31, 12, 5910-5925, 2021 · <a href="/1525.93268" class="nowrap">Zbl 1525.93268</a></td> </tr><tr> <td>[39]</td> <td class="space">Atrianfar, H.; Yadollahi, S., Event‐triggered adaptive sliding mode control for consensus of heterogeneous nonlinear multiagent systems, Int J Robust Nonlinear Control, 31, 18, 9294-9315, 2021 · <a href="/1527.93266" class="nowrap">Zbl 1527.93266</a></td> </tr><tr> <td>[40]</td> <td class="space">Wang, C.; Wen, C.; Hu, Q., Event‐triggered adaptive control for a class of nonlinear systems with unknown control direction and sensor faults, IEEE Trans Automat Contr, 65, 2, 763-770, 2019 · <a href="/1533.93505" class="nowrap">Zbl 1533.93505</a></td> </tr><tr> <td>[41]</td> <td class="space">Jin, X.; Haddad, WM; Yucelen, T., An adaptive control architecture for mitigating sensor and actuator attacks in cyber‐physical systems, IEEE Trans Automat Contr, 62, 11, 6058-6064, 2017 · <a href="/1390.93440" class="nowrap">Zbl 1390.93440</a></td> </tr><tr> <td>[42]</td> <td class="space">He, H.; Qi, W.; Liu, Z.; Wang, M., Adaptive attack‐resilient control for Markov jump system with additive attacks, Nonlinear Dyn, 103, 2, 1585-1598, 2021 · <a href="/1517.93050" class="nowrap">Zbl 1517.93050</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. 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Document Zbl 1534.93221 - zbMATH Open