Document Zbl 0908.93073

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The delays can be observed and their probability distribution is assumed to be known. Under a few additional hypotheses the authors derive optimal controls for a corresponding LQG problem. They provide an example which shows how their solution performs in comparison with other (suboptimal) controls proposed in the literature.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A5633">M.Scheutzow (Berlin)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1192906">Cited in <strong>174</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%3A93C83" title="MSC2020">93C83</a> </td> <td class="space"> Control/observation systems involving computers (process control, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C57" title="MSC2020">93C57</a> </td> <td class="space"> Sampled-data control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Arandom+delays">random delays</a>; <a href="/?q=ut%3Adelay+compensation">delay compensation</a>; <a href="/?q=ut%3Adistributed+computer+control+systems">distributed computer control systems</a>; <a href="/?q=ut%3Areal-time+systems">real-time systems</a>; <a href="/?q=ut%3Astochastic+control">stochastic control</a>; <a href="/?q=ut%3Astochastic+parameters">stochastic parameters</a>; <a href="/?q=ut%3Atiming+jitter">timing jitter</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 0908.93073" data-ciurl="/ci/01192906" data-biburl="/bibtex/01192906.bib" data-amsurl="/amsrefs/01192906.bib" data-xmlurl="/xml/01192906.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01192906.pdf" title="Zbl 0908.93073 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/S0005-1098(97)00170-2" aria-label="DOI for “Stochastic analysis and control of real-time systems with random time delays”" title="10.1016/S0005-1098(97)00170-2">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">Anderson, B. D.O.; Moore, J. B., Optimal Filtering (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · <a href="/0758.93070" class="nowrap">Zbl 0758.93070</a></td> </tr><tr> <td>[2]</td> <td class="space">Åström, K. J., Introduction to Stochastic Control Theory (1970), Academic Press: Academic Press New York, Translated into Russian, Japanese and Chinese · <a href="/0537.93048" class="nowrap">Zbl 0537.93048</a></td> </tr><tr> <td>[3]</td> <td class="space">Åström, K. J.; Wittenmark, Björn, Computer Controlled Systems—Theory and Design (1990), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ</td> </tr><tr> <td>[4]</td> <td class="space">Chan, H.; Özgüner, Ü., Closed-loop control of systems ver a communications network with queues, Int. J. Control, 62, 3, 493-510 (1995) · <a href="/0830.93055" class="nowrap">Zbl 0830.93055</a></td> </tr><tr> <td>[5]</td> <td class="space">Chen, H.-F.; Kumar, P. R.; van Schuppen, J. H., On Kalman filtering for conditionally Gaussian systems with random matrices, Systems Control Lett., 397-404 (1989) · <a href="/0697.93058" class="nowrap">Zbl 0697.93058</a></td> </tr><tr> <td>[6]</td> <td class="space">Doyle, J. C.; Stein, G., Robustness with observers, IEEE Trans. Automat. Control, AC-24, 4, 607-611 (1979) · <a href="/0412.93030" class="nowrap">Zbl 0412.93030</a></td> </tr><tr> <td>[7]</td> <td class="space">Ji, Y.; Chizeck, H. J.; Feng, X.; Loparo, K. A., Stability and control of discrete-time jump linear systems, Control Theory Adv. Technol., 7, 2, 247-270 (1991)</td> </tr><tr> <td>[8]</td> <td class="space">Kalman, R. E., Control of randomly varying linear dynamical systems, (Proc. Symp. in Appl. Math., 13 (1962)), 287-298 · <a href="/0107.35102" class="nowrap">Zbl 0107.35102</a></td> </tr><tr> <td>[9]</td> <td class="space">Krtolica, R.; Özgüner, Ü.; Chan, H.; Goktas, H.; Winkelman, J.; Liubakka, M., Stability of linear feedback systems with random communication delays, Int. J. Control, 59, 4, 925-953 (1994) · <a href="/0812.93073" class="nowrap">Zbl 0812.93073</a></td> </tr><tr> <td>[10]</td> <td class="space">Luck, R.; Ray, A., An observer-based compensator for distributed delays, Automatica, 26, 5, 903-908 (1990) · <a href="/0701.93055" class="nowrap">Zbl 0701.93055</a></td> </tr><tr> <td>[11]</td> <td class="space">Nilsson, J., Analysis and design of real-time systems with random delays, (LicTech Thesis (1996), Department of Automatic Control, Lund Institute of Technology: Department of Automatic Control, Lund Institute of Technology Lund, Sweden)</td> </tr><tr> <td>[12]</td> <td class="space">Nilsson, J.; Bernhardsson, B.; Wittenmark, B., Stochastic analysis and control of real-time systems with random time delays, (Proc. 13th Int. Federation of Automatic Control World Congress. Proc. 13th Int. Federation of Automatic Control World Congress, San Francisco (1996)), 267-272</td> </tr><tr> <td>[13]</td> <td class="space">Ray, A., Introduction to networking for integrated control systems, IEEE Control Systems Mag., 76-79 (1989)</td> </tr><tr> <td>[14]</td> <td class="space">Ray, A., Output feedback control under randomly varying distributed delays, J. Guidance Control Dyn., 17, 4, 701-711 (1994) · <a href="/0925.93291" class="nowrap">Zbl 0925.93291</a></td> </tr><tr> <td>[15]</td> <td class="space">Shin, K. G.; Kim, H., Hard deadlines in real-time systems, (IFAC Symp. on Algorithms and Architectures for Real-Time Control. IFAC Symp. on Algorithms and Architectures for Real-Time Control, Seoul, Korea (1992)), 9-14</td> </tr><tr> <td>[16]</td> <td class="space">Wittenmark, B.; Nilsson, J.; Törngren, M., Timing problems in real-time control systems, (Preprints American Control Conf. (1995)), 2000-2004, Seattle, WA, June</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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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