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Franklin Inst.</a> <a href="/?q=in%3A368515" title="Articles in this Issue">354, No. 12, 4784-4800 (2017)</a>. </div> <div class="abstract">Summary: This paper considers the distributed adaptive fault-tolerant control problem for linear multi-agent systems with matched unknown nonlinear functions and actuator bias faults. By using fuzzy logic systems to approximate the unknown nonlinear function and constructing a local observer to estimate the states, an effective distributed adaptive fault-tolerant controller is developed. Furthermore, different from the traditional method to estimate the weight matrix, only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems. In contrast to the existing results, the assumption that the dimensions of input vector and output vector are equal is removed. In addition, it is proved that the proposed control protocol guarantees all signals in the closed-loop systems are bounded and all agents converge to the leader with bounded residual errors. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6754217">Cited in <strong>16</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%3A68T42" title="MSC2020">68T42</a> </td> <td class="space"> Agent technology and artificial intelligence </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adistributed+adaptive+fault-tolerant+control">distributed adaptive fault-tolerant control</a>; <a href="/?q=ut%3Alinear+multi-agent+systems">linear multi-agent systems</a>; <a href="/?q=ut%3Amatched+unknown+nonlinear+functions">matched unknown nonlinear functions</a>; <a href="/?q=ut%3Aactuator+bias+faults">actuator bias faults</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 1367.93159" data-ciurl="/ci/06754217" data-biburl="/bibtex/06754217.bib" data-amsurl="/amsrefs/06754217.bib" data-xmlurl="/xml/06754217.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06754217.pdf" title="Zbl 1367.93159 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.jfranklin.2017.05.034" aria-label="DOI for “Adaptive fault-tolerant control for a class of nonlinear multi-agent systems with actuator faults”" title="10.1016/j.jfranklin.2017.05.034">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">Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 1, 215-233 (2007) &middot; <a href="/1376.68138" class="nowrap">Zbl 1376.68138</a></td> </tr><tr> <td>[2]</td> <td class="space">Ren, W., Information consensus in multivehicle cooperative control, IEEE Trans. Control Syst. Mag., 27, 2, 71-82 (2007)</td> </tr><tr> <td>[3]</td> <td class="space">Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Trans. Autom. Control, 49, 9, 1465-1476 (2004) &middot; <a href="/1365.90056" class="nowrap">Zbl 1365.90056</a></td> </tr><tr> <td>[4]</td> <td class="space">Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49, 9, 1520-1533 (2004) &middot; <a href="/1365.93301" class="nowrap">Zbl 1365.93301</a></td> </tr><tr> <td>[5]</td> <td class="space">Yu, W. W.; Chen, G. R.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) &middot; <a href="/1192.93019" class="nowrap">Zbl 1192.93019</a></td> </tr><tr> <td>[6]</td> <td class="space">Hong, Y. G.; Hu, J. P.; Gao, L. X., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182 (2006) &middot; <a href="/1117.93300" class="nowrap">Zbl 1117.93300</a></td> </tr><tr> <td>[7]</td> <td class="space">Zhu, W.; Cheng, D. Z., Leader-following consensus of second-order agents with multiple time-varying delays, Automatica, 46, 12, 1994-1999 (2010) &middot; <a href="/1205.93056" class="nowrap">Zbl 1205.93056</a></td> </tr><tr> <td>[8]</td> <td class="space">Li, Z. K.; Duan, Z. S.; Chen, G. R.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE Trans. Circuits Syst. I: Reg. Pap., 57, 1, 213-224 (2010) &middot; <a href="/1468.93137" class="nowrap">Zbl 1468.93137</a></td> </tr><tr> <td>[9]</td> <td class="space">Hou, Z. G.; Cheng, L.; Tan, M., Decentralized robust adaptive control for the multiagent system consensus problem using neural networks, IEEE Trans. Syst. Man. Cybern. B: Cybern., 39, 3, 636-647 (2009)</td> </tr><tr> <td>[10]</td> <td class="space">Das, A.; Lewis, F. L., Distributed adaptive control for synchronization of unknown nonlinear networked systems, Automatica, 46, 12, 2014-2021 (2010) &middot; <a href="/1205.93045" class="nowrap">Zbl 1205.93045</a></td> </tr><tr> <td>[11]</td> <td class="space">Cheng, L.; Hou, Z. G.; Tan, M.; Lin, Y. Z.; Zhang, W. J., Neural-network-based adaptive leader-following control for multiagent systems with uncertainties, IEEE Trans. Neural Netw., 21, 8, 1351-1358 (2010)</td> </tr><tr> <td>[12]</td> <td class="space">Hu, G. Q., Robust consensus tracking of a class of second-order multi-agent dynamic systems, Syst. Control Lett., 61, 1, 134-142 (2012) &middot; <a href="/1250.93009" class="nowrap">Zbl 1250.93009</a></td> </tr><tr> <td>[13]</td> <td class="space">Zhang, H. W.; Lewis, F. L., Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics, Automatica, 48, 7, 1432-1439 (2012) &middot; <a href="/1348.93144" class="nowrap">Zbl 1348.93144</a></td> </tr><tr> <td>[14]</td> <td class="space">Shen, Q. K.; Jiang, B.; Shi, P.; Zhao, J., Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time-varying actuator faults, IEEE Trans. Fuzzy Syst., 22, 3, 494-504 (2014)</td> </tr><tr> <td>[15]</td> <td class="space">Cui, R.; Ren, B.; Ge, S. S., Synchronised tracking control of multi-agent system with high order dynamics, IET Control Theory Appl., 6, 5, 603-614 (2012)</td> </tr><tr> <td>[16]</td> <td class="space">Peng, Z. H.; Wang, W.; Zhang, H. W.; Sun, G., Distributed neural network control for adaptive synchronization of uncertain dynamical multiagent systems, IEEE Trans. Neural Netw. Learn. Syst., 25, 8, 1508-1519 (2014)</td> </tr><tr> <td>[17]</td> <td class="space">Peng, Z. H.; Wang, D.; Sun, G.; Wang, H., Distributed cooperative stabilisation of continuous-time uncertain nonlinear multi-agent systems, Int. J. Syst. Sci., 45, 10, 2031-2041 (2014) &middot; <a href="/1317.93018" class="nowrap">Zbl 1317.93018</a></td> </tr><tr> <td>[18]</td> <td class="space">Wang, W.; Wang, D.; Peng, Z. H., Cooperative fuzzy adaptive output feedback control for synchronisation of nonlinear multi-agent systems under directed graphs, Int. J. Syst. Sci., 46, 16, 2982-2995 (2015) &middot; <a href="/1332.93220" class="nowrap">Zbl 1332.93220</a></td> </tr><tr> <td>[19]</td> <td class="space">Peng, Z. H.; Wang, D.; Zhang, H. W.; Lin, Y. J., Cooperative output feedback adaptive control of uncertain nonlinear multi-agent systems with a dynamic leader, Neurocomputing, 149, 132-141 (2015)</td> </tr><tr> <td>[20]</td> <td class="space">Veillette, R. J.; Medanic, J.; Perkins, W. R., Design of reliable control systems, IEEE Trans. Autom. Control, 37, 3, 290-304 (1992) &middot; <a href="/0745.93025" class="nowrap">Zbl 0745.93025</a></td> </tr><tr> <td>[21]</td> <td class="space">Su, X. J.; Shi, P.; Wu, L. G.; Song, Y. D., Fault detection filtering for nonlinear switched stochastic systems, IEEE Trans. Autom. Control, 61, 5, 1310-1315 (2016) &middot; <a href="/1359.93497" class="nowrap">Zbl 1359.93497</a></td> </tr><tr> <td>[22]</td> <td class="space">Hameed, I.; El-Madbouly, E.; Abdo, M., Sensor and actuator fault-hiding reconfigurable control design for a four-tank system benchmark, Int. J. Innov. Comput. Inf. Control, 11, 2, 679-690 (2015)</td> </tr><tr> <td>[23]</td> <td class="space">Shi, P.; Liu, M.; Zhang, L. X., Fault-tolerant sliding-mode-observer synthesis of Markovian jump systems using quantized measurements, IEEE Trans. Ind. Electron., 62, 9, 5910-5918 (2015)</td> </tr><tr> <td>[24]</td> <td class="space">Tao, G.; Joshi, S. M.; Ma, X. L., Adaptive state feedback and tracking control of systems with actuator failures, IEEE Trans. Autom. Control, 46, 1, 78-95 (2001) &middot; <a href="/0992.93043" class="nowrap">Zbl 0992.93043</a></td> </tr><tr> <td>[25]</td> <td class="space">Yang, G. H.; Ye, D., Reliable control of linear systems with adaptive mechanism, IEEE Trans. Autom. Control, 55, 1, 242-247 (2010) &middot; <a href="/1368.93161" class="nowrap">Zbl 1368.93161</a></td> </tr><tr> <td>[26]</td> <td class="space">Jiang, B.; Staroswiecki, M.; Cocquempot, V., Fault accommodation for nonlinear dynamic systems, IEEE Trans. Autom. Control, 51, 9, 1578-1583 (2006) &middot; <a href="/1366.93694" class="nowrap">Zbl 1366.93694</a></td> </tr><tr> <td>[27]</td> <td class="space">Zhang, K.; Jiang, B.; Staroswiecki, M., Dynamic output feedback-fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults, IEEE Trans. Fuzzy Syst., 18, 1, 194-201 (2010)</td> </tr><tr> <td>[28]</td> <td class="space">Huang, S. J.; Yang, G. H., Fault tolerant controller design for T-S fuzzy systems with time-varying delay and actuator faults: a K-step fault-estimation approach, IEEE Trans. Fuzzy Syst., 22, 6, 1526-1540 (2014)</td> </tr><tr> <td>[29]</td> <td class="space">Semsar-Kazerooni, E.; Khorasani, K., Optimal consensus algorithms for cooperative team of agents subject to partial information, Automatica, 44, 11, 2766-2777 (2008) &middot; <a href="/1194.49056" class="nowrap">Zbl 1194.49056</a></td> </tr><tr> <td>[30]</td> <td class="space">Yang, H.; Staroswiecki, M.; Jiang, B.; Liu, J. Y., Fault tolerant cooperative control for a class of nonlinear multi-agent systems, Syst. Control Lett., 60, 4, 271-277 (2011) &middot; <a href="/1216.93010" class="nowrap">Zbl 1216.93010</a></td> </tr><tr> <td>[31]</td> <td class="space">Wen, G. H.; Duan, Z. S.; Li, Z. K.; Chen, G. R., Stochastic consensus in directed networks of agents with non-linear dynamics and repairable actuator failures, IET Control Theory Appl., 6, 11, 1583-1593 (2012)</td> </tr><tr> <td>[32]</td> <td class="space">Semsar-Kazerooni, E.; Khorasani, K., Team consensus for a network of unmanned vehicles in presence of actuator faults, IEEE Trans. Control Syst. Technol., 18, 5, 1155-1161 (2010)</td> </tr><tr> <td>[33]</td> <td class="space">Zuo, Z. Q.; Zhang, J.; Wang, Y. J., Adaptive fault tolerant tracking control for linear and Lipschitz nonlinear multi-agent systems, IEEE Trans. Ind. Electron., 62, 6, 3923-3931 (2015)</td> </tr><tr> <td>[34]</td> <td class="space">Deng, C.; Yang, G. H., Distributed adaptive fault-tolerant containment control for a class of multi-agent systems with non-identical matching non-linear functions, IET Control Theory Appl., 10, 3, 273-281 (2016)</td> </tr><tr> <td>[35]</td> <td class="space">Wang, X.; Yang, G. H., Distributed reliable \(H_∞\) consensus control for a class of multi-agent systems under switching networks: A topology-based average dwell time approach, Int. J. Robust Nonlinear Control, 13, 26, 2767-2787 (2016) &middot; <a href="/1346.93042" class="nowrap">Zbl 1346.93042</a></td> </tr><tr> <td>[36]</td> <td class="space">Wang, X.; Yang, G. H., Distributed fault-tolerant control for a class of cooperative uncertain systems with actuator failures and switching topologies, Inf. Sci, 370-371, 650-666 (2016) &middot; <a href="/1429.93081" class="nowrap">Zbl 1429.93081</a></td> </tr><tr> <td>[37]</td> <td class="space">Wang, L. X.; Mendel, J. M., Fuzzy basis functions, universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Netw., 3, 5, 807-814 (1992)</td> </tr><tr> <td>[38]</td> <td class="space">Su, X. J.; Wu, L. G.; Shi, P.; Song, Y. D., A novel approach to output feedback control of fuzzy stochastic systems, Automatica, 50, 12, 3268-3275 (2014) &middot; <a href="/1309.93092" class="nowrap">Zbl 1309.93092</a></td> </tr><tr> <td>[39]</td> <td class="space">Mohamed, H. M.A. K.; Francois, D., On the global exponential stabilization of Takagi-Sugeno fuzzy uncertain systems, Int. J. Innov. Comput. Inf. Control, 11, 1, 679-690 (2015)</td> </tr><tr> <td>[40]</td> <td class="space">Li, Y. X.; Yang, G. H., Fuzzy adaptive output feedback fault-tolerant tracking control of a class of uncertain nonlinear systems with non-affine nonlinear faults, IEEE Trans. Fuzzy Syst., 24, 1, 223-234 (2016)</td> </tr><tr> <td>[41]</td> <td class="space">Li, T. S.; Wang, D.; Feng, G.; Tong, S. C., A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems, IEEE Trans. Syst. Man. Cybern. B: Cybern, 40, 3, 915-927 (2010)</td> </tr><tr> <td>[42]</td> <td class="space">Zhang, H. W.; Lewis, F. L.; Qu, Z. H., Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs, IEEE Trans. Ind. Electron., 59, 7, 3026-3041 (2012)</td> </tr><tr> <td>[43]</td> <td class="space">Wen, G. H.; Li, Z. K.; Duan, Z. S.; Chen, G. R., Distributed consensus control for linear multi-agent systems with discontinuous observations, Int. J. Control, 86, 1, 95-106 (2013) &middot; <a href="/1278.93017" class="nowrap">Zbl 1278.93017</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. 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