Document Zbl 1213.93203

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Control Appl. Methods</a> <a href="/?q=in%3A273608" title="Articles in this Issue">32, No. 1, 113-125 (2011)</a>. </div> <div class="abstract">Summary: The linear quadratic optimal stochastic control problem is investigated for multiparameter singularly perturbed stochastic systems in which N lower-level fast subsystems are interconnected by a higher-level slow subsystem. After establishing the asymptotic structure of the solution for the Multiparameter Stochastic Algebraic Riccati Equation (MSARE), a near-optimal controller that is independent of small unknown parameters is obtained by neglecting these parameters. The stability of a closed-loop stochastic system is investigated. Furthermore, it is shown that the resulting controller achieves an $O(\|\nu \|^{2})$ approximation to the optimal cost of the original control problem. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example – a practical multi-area power system – is solved.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5866105">Cited in <strong>6</strong> Documents</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%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%3A93C70" title="MSC2020">93C70</a> </td> <td class="space"> Time-scale analysis and singular perturbations in control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amultiparameter+singularly+perturbed+stochastic+systems+%28MSPSS%29">multiparameter singularly perturbed stochastic systems (MSPSS)</a>; <a href="/?q=ut%3Alinear+quadratic+optimal+stochastic+control">linear quadratic optimal stochastic control</a>; <a href="/?q=ut%3Aparameter+independent+controller">parameter independent controller</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 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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/oca.934" aria-label="DOI for “Near-optimal control for multiparameter singularly perturbed stochastic systems”" title="10.1002/oca.934">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">Khalil, Control strategies for decision makers using different models of the same system, IEEE Transactions on Automatic Control 23 (2) pp 289– (1978) · <a href="/0384.93007" class="nowrap">Zbl 0384.93007</a> · <a href="https://doi.org/10.1109/TAC.1978.1101712" class="nowrap">doi:10.1109/TAC.1978.1101712</a></td> </tr><tr> <td>[2]</td> <td class="space">Khalil, Control of linear systems with multiparameter singular perturbations, Automatica 15 (2) pp 197– (1979) · <a href="/0409.93019" class="nowrap">Zbl 0409.93019</a> · <a 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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