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The controller online optimizes a free control move followed by an output feedback control law based on the pre-specified state estimator. A key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem. The Quadratic Boundedness (QB) of the augmented state is guaranteed by the proposed approach. A numerical example is given to illustrate the effectiveness of the proposed controller.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6372118">Cited in <strong>11</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B35" title="MSC2020">93B35</a> </td> <td class="space"> Sensitivity (robustness) </td> </tr><tr> <td class="mono"> 93B40 </td> <td class="space"> Computational methods in systems theory (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C05" title="MSC2020">93C05</a> </td> <td class="space"> Linear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E10" title="MSC2020">93E10</a> </td> <td class="space"> Estimation and detection in stochastic control theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Amodel+predictive+control">model predictive control</a>; <a href="/?q=ut%3Astate+estimator">state estimator</a>; <a href="/?q=ut%3Aoutput+feedback">output feedback</a>; <a href="/?q=ut%3Alinear+polytopic+uncertain+model">linear polytopic uncertain model</a>; <a href="/?q=ut%3Alinear+matrix+inequality">linear matrix inequality</a>; <a href="/?q=ut%3Astate+estimator.">state estimator.</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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">&times;</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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1300.93057" data-ciurl="/ci/06372118" data-biburl="/bibtex/06372118.bib" data-amsurl="/amsrefs/06372118.bib" data-xmlurl="/xml/06372118.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06372118.pdf" title="Zbl 1300.93057 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/j.automatica.2014.10.021" aria-label="DOI for “Output feedback robust MPC with one free control move for the linear polytopic uncertain system with bounded disturbance”" title="10.1016/j.automatica.2014.10.021">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">Alessandri, A.; Baglietto, M.; Battistelli, G., On estimation error bounds for receding-horizon filters using quadratic boundedness, IEEE Transactions on Automatic Control, 49, 1350-1355 (2004) &middot; <a href="/1365.93495" class="nowrap">Zbl 1365.93495</a></td> </tr><tr> <td>[2]</td> <td class="space">Alessandri, A.; Baglietto, M.; Battistelli, G., Design of state estimators for uncertain linear systems using quadratic boundedness, Automatica, 42, 497-502 (2006) &middot; <a href="/1123.93052" class="nowrap">Zbl 1123.93052</a></td> </tr><tr> <td>[3]</td> <td class="space">Besselmann, T.; Löfberg, J.; Morari, M., Explicit MPC for LPV systems: stability and optimality, IEEE Transactions on Automatic Control, 57, 2322-2332 (2012) &middot; <a href="/1369.93331" class="nowrap">Zbl 1369.93331</a></td> </tr><tr> <td>[4]</td> <td class="space">Betti, G.; Farina, M.; Scattolini, R., A robust MPC algorithm for offset-free tracking of constant reference signals, IEEE Transactions on Automatic Control, 58, 2394-2400 (2013) &middot; <a href="/1369.93332" class="nowrap">Zbl 1369.93332</a></td> </tr><tr> <td>[5]</td> <td class="space">Bumroongsri, P.; Kheawhom, S., An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes, Systems &amp; Control Letters, 61, 435-442 (2012) &middot; <a href="/1250.93053" class="nowrap">Zbl 1250.93053</a></td> </tr><tr> <td>[6]</td> <td class="space">Casavola, A.; Famularo, D.; Franzè, G.; Garone, E., A fast ellipsoidal MPC scheme for discrete-time polytopic linear parameter varying systems, Automatica, 48, 2620-2626 (2012) &middot; <a href="/1271.93056" class="nowrap">Zbl 1271.93056</a></td> </tr><tr> <td>[7]</td> <td class="space">Ding, B., Homogeneous polynomially nonquadratic stabilization of discrete-time Takagi-Sugeno systems via nonparallel distributed compensation law, IEEE Transactions on Fuzzy Systems, 18, 994-1000 (2010)</td> </tr><tr> <td>[8]</td> <td class="space">Ding, B., Properties of parameter-dependent open-loop MPC for uncertain systems with polytopic description, Asian Journal of Control, 12, 58-70 (2010)</td> </tr><tr> <td>[9]</td> <td class="space">Ding, B., Dynamic output feedback predictive control for nonlinear systems represented by a Takagi-Sugeno model, IEEE Transactions on Fuzzy Systems, 19, 831-843 (2011)</td> </tr><tr> <td>[10]</td> <td class="space">Ding, B.; Ping, X.; Pan, H., On dynamic output feedback robust MPC for constrained quasi-LPV systems, International Journal of Control, 86, 2215-2227 (2013) &middot; <a href="/1311.93026" class="nowrap">Zbl 1311.93026</a></td> </tr><tr> <td>[11]</td> <td class="space">Gao, Y.; Chong, K. T., The explicit constrained min-max model predictive control of a discrete-time linear system with uncertain disturbances, IEEE Transactions on Automatic Control, 57, 2373-2378 (2012) &middot; <a href="/1369.93338" class="nowrap">Zbl 1369.93338</a></td> </tr><tr> <td>[12]</td> <td class="space">Garone, E.; Casavola, A., Receding horizon control strategies for constrained LPV systems based on a class of nonlinearly parameterized Lyapunov functions, IEEE Transactions on Automatic Control, 57, 2354-2360 (2012) &middot; <a href="/1369.93339" class="nowrap">Zbl 1369.93339</a></td> </tr><tr> <td>[13]</td> <td class="space">Gautam, A.; Chu, Y. C.; Soh, Y. C., Optimized dynamic policy for receding horizon control of linear time-varying systems with bounded disturbances, IEEE Transactions on Automatic Control, 57, 973-988 (2012) &middot; <a href="/1369.93340" class="nowrap">Zbl 1369.93340</a></td> </tr><tr> <td>[14]</td> <td class="space">Ghaemi, R.; Sun, J.; Kolmanovsky, I. V., Robust control of constrained linear systems with bounded disturbances, IEEE Transactions on Automatic Control, 57, 2683-2688 (2012) &middot; <a href="/1369.93234" class="nowrap">Zbl 1369.93234</a></td> </tr><tr> <td>[15]</td> <td class="space">Kothare, M. V.; Balakrishnan, V.; Morari, M., Robust constrained model predictive control using linear matrix inequalities, Automatica, 32, 1361-1379 (1996) &middot; <a href="/0897.93023" class="nowrap">Zbl 0897.93023</a></td> </tr><tr> <td>[16]</td> <td class="space">Li, H.; Shi, Y., Output feedback predictive control for constrained linear systems with intermittent measurements, Systems &amp; Control Letters, 62, 345-354 (2013) &middot; <a href="/1261.93041" class="nowrap">Zbl 1261.93041</a></td> </tr><tr> <td>[17]</td> <td class="space">Li, D.; Xi, Y.; Gao, F., Synthesis of dynamic output feedback RMPC with saturated inputs, Automatica, 49, 949-954 (2013) &middot; <a href="/1284.93102" class="nowrap">Zbl 1284.93102</a></td> </tr><tr> <td>[18]</td> <td class="space">Lu, Y.; Arkun, Y., Quasi-min-max MPC algorithms for LPV systems, Automatica, 36, 527-540 (2000) &middot; <a href="/0981.93027" class="nowrap">Zbl 0981.93027</a></td> </tr><tr> <td>[19]</td> <td class="space">Mayne, D. Q.; Raković, S. V.; Findeisen, R.; Allgöwer, F., Robust output feedback model predictive control of constrained linear systems, Automatica, 42, 1217-1222 (2006) &middot; <a href="/1116.93032" class="nowrap">Zbl 1116.93032</a></td> </tr><tr> <td>[20]</td> <td class="space">Mayne, D. Q.; Raković, S. V.; Findeisen, R.; Allgöwer, F., Robust output feedback model predictive control of constrained linear systems: time varying case, Automatica, 45, 2082-2087 (2009) &middot; <a href="/1175.93072" class="nowrap">Zbl 1175.93072</a></td> </tr><tr> <td>[21]</td> <td class="space">Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: stability and optimality, Automatica, 36, 789-814 (2000) &middot; <a href="/0949.93003" class="nowrap">Zbl 0949.93003</a></td> </tr><tr> <td>[22]</td> <td class="space">Nguyen, H. N.; Gutman, P. O.; Olaru, S.; Hovd, M., Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints, IEEE Transactions on Automatic Control, 58, 2754-2759 (2013) &middot; <a href="/1364.93687" class="nowrap">Zbl 1364.93687</a></td> </tr><tr> <td>[23]</td> <td class="space">Park, J. H.; Kim, T. H.; Sugie, T., Output feedback model predictive control for LPV systems based on quasi-min-max algorithm, Automatica, 47, 2052-2058 (2011) &middot; <a href="/1229.93056" class="nowrap">Zbl 1229.93056</a></td> </tr><tr> <td>[24]</td> <td class="space">Raković, S. V.; Kouvaritakis, B.; Cannon, M.; Panos, C.; Findeisen, R., Parameterized tube model predictive control, IEEE Transactions on Automatic Control, 57, 2746-2761 (2012) &middot; <a href="/1369.93240" class="nowrap">Zbl 1369.93240</a></td> </tr><tr> <td>[25]</td> <td class="space">Raković, S. V.; Kouvaritakis, B.; Findeisen, R.; Cannon, M., Homothetic tube model predictive control, Automatica, 48, 1631-1638 (2012) &middot; <a href="/1267.93049" class="nowrap">Zbl 1267.93049</a></td> </tr><tr> <td>[26]</td> <td class="space">Sala, A.; Ariño, C., Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: application of Polya’s theorem, Fuzzy Sets and Systems, 158, 2671-2686 (2007) &middot; <a href="/1133.93348" class="nowrap">Zbl 1133.93348</a></td> </tr><tr> <td>[27]</td> <td class="space">Su, Y.; Tan, K. K., Comments on &ldquo;Output feedback model predictive control for LPV systems based on quasi-min-max algorithm&rdquo;, Automatica, 48, 2385 (2012) &middot; <a href="/1257.93038" class="nowrap">Zbl 1257.93038</a></td> </tr><tr> <td>[28]</td> <td class="space">Voelker, A.; Kouramas, K.; Pistikopoulos, E. N., Simultaneous design of explicit/multi-parametric constrained moving horizon estimation and robust model predictive control, Computers &amp; Chemical Engineering, 54, 24-33 (2013)</td> </tr><tr> <td>[29]</td> <td class="space">Yu, S.; Röhm, C.; Chen, H.; Allgöwer, F., Model predictive control of constrained LPV systems, International Journal of Control, 85, 671-683 (2012) &middot; <a href="/1256.93039" class="nowrap">Zbl 1256.93039</a></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&nbsp;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"> &copy; 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 &amp; 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">&nbsp;<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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