Document Zbl 1205.93045

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A design method is presented for adaptive synchronization controllers for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown. The development is for strongly connected digraph communication structures. A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol. The proper selection of the Lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion. Lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the Frobenius norm. The resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node. Singular value analysis is used. It is shown that the singular values of certain key matrices are intimately related to structural properties of the graph.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5850206">Cited in <strong>169</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B51" title="MSC2020">93B51</a> </td> <td class="space"> Design techniques (robust design, computer-aided design, etc.) </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%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+multiagent+systems">nonlinear multiagent systems</a>; <a href="/?q=ut%3Adistributed+adaptive+control">distributed adaptive control</a>; <a href="/?q=ut%3Asynchronization">synchronization</a>; <a href="/?q=ut%3Aconsensus">consensus</a>; <a href="/?q=ut%3Anetworked+systems">networked 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 1205.93045" data-ciurl="/ci/05850206" data-biburl="/bibtex/05850206.bib" data-amsurl="/amsrefs/05850206.bib" data-xmlurl="/xml/05850206.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05850206.pdf" title="Zbl 1205.93045 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.2010.08.008" aria-label="DOI for “Distributed adaptive control for synchronization of unknown nonlinear networked systems”" title="10.1016/j.automatica.2010.08.008">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">Bernstein, D., Matrix mathematics (2005), Princeton Univ. 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