Document Zbl 1490.76162

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J. Comput. Math.</a> <a href="/?q=in%3A477024" title="Articles in this Issue">97, No. 7, 1529-1544 (2020)</a>. </div> <div class="abstract">Summary: In this paper, a new numerical scheme is constructed to solve a class of Infinite Horizon Optimal Control Problems (IHOCPs). The idea is to extend the spectral Ritz method to solve an IHOCP directly by a proper approximation of the state and control functions. We solve the IHOCP on the original time interval. Applying the new constructed operational Laguerre matrix and substituting the estimated functions into the performance index yields a system of algebraic equations. Notably, the choice of Laguerre polynomials along with the spectral Ritz method provides to impose all the given initial and boundary conditions easily. By rigorous proofs, the convergence of the new method is investigated. The numerical technique is also examined by adding three illustrative application problems to show the applicability and effectiveness of the proposed technique. Furthermore, our results are compared with the outlets of other works to show superiority of the proposed methodology.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7476008">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%3A76M22" title="MSC2020">76M22</a> </td> <td class="space"> Spectral methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A49J15" title="MSC2020">49J15</a> </td> <td class="space"> Existence theories for optimal control problems involving ordinary differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A33C45" title="MSC2020">33C45</a> </td> <td class="space"> Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainfinite+horizon+optimal+control+problems+%28IHOCPs%29">infinite horizon optimal control problems (IHOCPs)</a>; <a href="/?q=ut%3Aspectral+Ritz+method">spectral Ritz method</a>; <a href="/?q=ut%3ALaguerre+polynomial">Laguerre polynomial</a>; <a href="/?q=ut%3Aconvergence">convergence</a>; <a href="/?q=ut%3Amultivariable+optimization">multivariable optimization</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 1490.76162" data-ciurl="/ci/07476008" data-biburl="/bibtex/07476008.bib" data-amsurl="/amsrefs/07476008.bib" data-xmlurl="/xml/07476008.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07476008.pdf" title="Zbl 1490.76162 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/10.1080/00207160.2019.1628949" aria-label="DOI for “A new approach for solving infinite horizon optimal control problems using Laguerre functions and Ritz spectral method”" title="10.1080/00207160.2019.1628949">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">Abualrub, T.; Abukhaled, M., Wavelets approach for optimal boundary control of cellular uptake in tissue engineering, Int. 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