Document Zbl 0949.93003

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Q.</a>; <a href="/authors/rawlings.james-b" title="Author Profile">Rawlings, J. B.</a>; <a href="/authors/rao.christopher-v" title="Author Profile">Rao, C. V.</a>; <a href="/authors/scokaert.pierre-o-m" title="Author Profile">Scokaert, P. O. M.</a></div> <h2 class="title"> <strong>Constrained model predictive control: Stability and optimality.</strong> <i>(English)</i> <a class="label nowrap" href="/0949.93003">Zbl 0949.93003</a> </h2> <div class="source"> <a href="/serials/348" title="Journal Profile">Automatica</a> <a href="/?q=in%3A64908" title="Articles in this Issue">36, No. 6, 789-814 (2000)</a>; correction ibid. 37, 483 (2001). </div> <div class="abstract">Summary: Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. An important advantage of this type of control is its ability to cope with hard constraints on controls and states. It has, therefore, been widely applied in petro-chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls. In this review, we focus on model predictive control of constrained systems, both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and/or time-varying systems. We concentrate our attention on research dealing with stability and optimality; in these areas the subject has developed, in our opinion, to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control. We distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature. In some cases the finite horizon optimal control problem solved on-line is exactly equivalent to the same problem with an infinite horizon; in other cases it is equivalent to a modified infinite horizon optimal control problem. In both situations, known advantages of infinite horizon optimal control accrue.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1443871">Cited in <strong>1000</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93-02" title="MSC2020">93-02</a> </td> <td class="space"> Research exposition (monographs, survey articles) pertaining to systems and control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B51" title="MSC2020">93B51</a> </td> <td class="space"> Design techniques (robust design, computer-aided design, etc.) </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%3Aconstrained+systems">constrained systems</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Aoptimality">optimality</a>; <a href="/?q=ut%3Ainfinite+horizon">infinite horizon</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 0949.93003" data-ciurl="/ci/01443871" data-biburl="/bibtex/01443871.bib" data-amsurl="/amsrefs/01443871.bib" data-xmlurl="/xml/01443871.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01443871.pdf" title="Zbl 0949.93003 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(99)00214-9" aria-label="DOI for “Constrained model predictive control: Stability and optimality”" title="10.1016/S0005-1098(99)00214-9">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">Alamir, M.; Bornard, G., Stability of a truncated infinite constrained receding horizon schemeThe general discrete nonlinear case, Automatica, 31, 9, 1353-1356 (1995) · <a href="/0831.93055" class="nowrap">Zbl 0831.93055</a></td> </tr><tr> <td>[2]</td> <td class="space">Allgöwer, F., & Zheng, A. 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