Document Zbl 1409.34056

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Appl. Math.</a> <a href="/?q=in%3A426650" title="Articles in this Issue">79, No. 1, 111-130 (2019)</a>. </div> <div class="abstract">Summary: In this paper we investigate the finite-time and fixed-time consensus problems of multiagent networks with pinning control and noise perturbation. In order to reach the finite-time and fixed-time consensus, several pinning protocols are proposed. Compared with the consensus protocols without pinning control, the proposed finite-time and fixed-time protocols need to control only a small fraction of agents, which is practical and has advantages from the physical viewpoint of energy consumption. More specifically, the deterministic and stochastic protocols include the graph $(p+1)$-Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that, unlike the protocols with the standard (linear) graph Laplacian, those with the graph $(p+1)$-Laplacian solve the finite-time as well as the fixed-time consensus problems. By using the finite-time and fixed-time stability theory and the algebra graph theory, sufficient conditions are established to ensure the finite-time and fixed-time consensus. Finally, numerical simulations are presented to illustrate the correctness of the theoretical results.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7008887">Cited in <strong>18</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A34H05" title="MSC2020">34H05</a> </td> <td class="space"> Control problems involving ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34F05" title="MSC2020">34F05</a> </td> <td class="space"> Ordinary differential equations and systems with randomness </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34C05" title="MSC2020">34C05</a> </td> <td class="space"> Topological structure of integral curves, singular points, limit cycles of ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A34D06" title="MSC2020">34D06</a> </td> <td class="space"> Synchronization of solutions to ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92B25" title="MSC2020">92B25</a> </td> <td class="space"> Biological rhythms and synchronization </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E15" title="MSC2020">93E15</a> </td> <td class="space"> Stochastic stability in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92B20" title="MSC2020">92B20</a> </td> <td class="space"> Neural networks for/in biological studies, artificial life and related topics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconsensus">consensus</a>; <a href="/?q=ut%3Acollective+behavior">collective behavior</a>; <a href="/?q=ut%3Amultiagent+system">multiagent system</a>; <a href="/?q=ut%3Anoise">noise</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 1409.34056" data-ciurl="/ci/07008887" data-biburl="/bibtex/07008887.bib" data-amsurl="/amsrefs/07008887.bib" data-xmlurl="/xml/07008887.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07008887.pdf" title="Zbl 1409.34056 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/10.1137/18M1174143" aria-label="DOI for “Finite-time and fixed-time consensus of multiagent networks with pinning control and noise perturbation”" title="10.1137/18M1174143">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://eprints.whiterose.ac.uk/139979/8/18m1174143.pdf" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">I. 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