Document Zbl 07892474

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Control</a> <a href="/?q=in%3A515657" title="Articles in this Issue">26, No. 1, 481-489 (2024)</a>. </div> <div class="abstract">Summary: This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. Combining the Kronecker product theory with an existing policy iteration algorithm, a data-driven policy iteration algorithm is proposed to solve the problem. In contrast to most existing methods that need all information of system coefficients, the proposed algorithm eliminates the requirement of three system matrices by utilizing data of a stochastic system. More specifically, this algorithm uses the collected data to iteratively approximate the optimal control and a solution of the stochastic algebraic Riccati equation (SARE) corresponding to the SLQ optimal control problem. The convergence analysis of the obtained algorithm is given rigorously, and a simulation example is provided to illustrate the effectiveness and applicability of the algorithm.<br class="zbmathjax-paragraph">© 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7892474">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%3A49K45" title="MSC2020">49K45</a> </td> <td class="space"> Optimality conditions for problems involving randomness </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49N10" title="MSC2020">49N10</a> </td> <td class="space"> Linear-quadratic optimal control problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B47" title="MSC2020">93B47</a> </td> <td class="space"> Iterative learning control </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93D15" title="MSC2020">93D15</a> </td> <td class="space"> Stabilization of systems by feedback </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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adata-driven">data-driven</a>; <a href="/?q=ut%3Apolicy+iteration">policy iteration</a>; <a href="/?q=ut%3Astochastic+algebraic+Riccati+equation">stochastic algebraic Riccati equation</a>; <a href="/?q=ut%3Astochastic+linear-quadratic+optimal+control+problem">stochastic linear-quadratic optimal control problem</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 07892474" data-ciurl="/ci/07892474" data-biburl="/bibtex/07892474.bib" data-amsurl="/amsrefs/07892474.bib" data-xmlurl="/xml/07892474.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07892474.pdf" title="Zbl 07892474 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/asjc.3223" aria-label="DOI for “Data-driven policy iteration algorithm for continuous-time stochastic linear-quadratic optimal control problems”" title="10.1002/asjc.3223">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2209.14490"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Kalman, R. 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