Document Zbl 1087.49022

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It is shown that the constrained optimal control law has the largest region of asymptotic stability (RAS). The value function of this HJB equation is solved by solving a sequence of cost functions satisfying a sequence of Lyapunov equations (LE). A neural network is used to approximate the cost function associated with each LE using the method of least-squares on a well-defined region of attraction of an initial stabilizing controller. As the order of the neural network is increased, the least-squares solution of the HJB equation converges uniformly to the exact solution of the inherently nonlinear HJB equation associated with the saturating control inputs. The result is a nearly optimal constrained state feedback controller that has been tuned a priori off-line.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A2236392">Cited in <strong>188</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A49L20" title="MSC2020">49L20</a> </td> <td class="space"> Dynamic programming in optimal control and differential games </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C10" title="MSC2020">93C10</a> </td> <td class="space"> Nonlinear systems in control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A92B20" title="MSC2020">92B20</a> </td> <td class="space"> Neural networks for/in biological studies, artificial life and related topics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aactuator+saturation">actuator saturation</a>; <a href="/?q=ut%3Aconstrained+input+systems">constrained input systems</a>; <a href="/?q=ut%3Ainfinite+horizon+control">infinite horizon control</a>; <a href="/?q=ut%3AHamilton-Jacobi-Bellman+equation">Hamilton-Jacobi-Bellman equation</a>; <a href="/?q=ut%3ALyapunov+equation">Lyapunov equation</a>; <a href="/?q=ut%3Aleast+squares">least squares</a>; <a href="/?q=ut%3Aneural+network">neural network</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 1087.49022" data-ciurl="/ci/02236392" data-biburl="/bibtex/02236392.bib" data-amsurl="/amsrefs/02236392.bib" data-xmlurl="/xml/02236392.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02236392.pdf" title="Zbl 1087.49022 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.2004.11.034" aria-label="DOI for “Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach”" title="10.1016/j.automatica.2004.11.034">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">Adams, R.; Fournier, J., Sobolev spaces (2003), Academic Press: Academic Press New York · <a href="/1098.46001" class="nowrap">Zbl 1098.46001</a></td> </tr><tr> <td>[2]</td> <td class="space">Apostol, T., Mathematical analysis (1974), Addison-Wesley: Addison-Wesley Reading, MA · <a href="/0309.26002" class="nowrap">Zbl 0309.26002</a></td> </tr><tr> <td>[3]</td> <td class="space">Bardi, M.; Capuzzo-Dolcetta, I., Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations (1997), Birkhauser: Birkhauser Boston, MA · <a href="/0890.49011" class="nowrap">Zbl 0890.49011</a></td> </tr><tr> <td>[4]</td> <td class="space">Beard, R. 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