Document Zbl 1520.93611

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J. Control</a> <a href="/?q=in%3A499989" title="Articles in this Issue">96, No. 8, 2133-2145 (2023)</a>. </div> <div class="abstract">Summary: In this paper, we derive stability margins for optimal and inverse optimal stochastic feedback regulators. Specifically, gain, sector, and disk margin guarantees are obtained for discrete-time nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal controllers that minimise a nonlinear-nonquadratic performance criterion. Furthermore, using the newly developed notion of stochastic dissipativity we derive a return difference inequality to provide connections between stochastic dissipativity and optimality of nonlinear controllers for discrete-time stochastic dynamical systems. In particular, using extended Kalman-Yakubovich-Popov conditions characterising stochastic dissipativity we show that our optimal feedback control law satisfies a return difference inequality predicated on a difference operator of a controlled Markov dispersion process and is stochastically dissipative with respect to a specific quadratic supply rate.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7716545">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E20" title="MSC2020">93E20</a> </td> <td class="space"> Optimal stochastic control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49N45" title="MSC2020">49N45</a> </td> <td class="space"> Inverse problems in optimal control </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%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%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Astochastic+dissipativity">stochastic dissipativity</a>; <a href="/?q=ut%3Acontrolled+Markov+chains">controlled Markov chains</a>; <a href="/?q=ut%3AKalman-Yakubovic-Popov+conditions">Kalman-Yakubovic-Popov conditions</a>; <a href="/?q=ut%3Ainverse+optimality">inverse optimality</a>; <a href="/?q=ut%3Again">gain</a>; <a href="/?q=ut%3Asensor">sensor</a>; <a href="/?q=ut%3Aand+disk+margins">and disk margins</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 1520.93611" data-ciurl="/ci/07716545" data-biburl="/bibtex/07716545.bib" data-amsurl="/amsrefs/07716545.bib" data-xmlurl="/xml/07716545.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07716545.pdf" title="Zbl 1520.93611 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/10.1080/00207179.2022.2085178" aria-label="DOI for “Dissipativity, inverse optimal control, and stability margins for nonlinear discrete-time stochastic feedback regulators”" title="10.1080/00207179.2022.2085178">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">Applebaum, D., Lévy processes and stochastic calculus (2009), Cambridge University Press · <a href="/1200.60001" class="nowrap">Zbl 1200.60001</a></td> </tr><tr> <td>[2]</td> <td class="space">Billingsley, P., Probability and measure (1995), J. 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