Document Zbl 07980544

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Even though there is a plethora of literature available for calculating MVLB for the linear systems, these methods are not suitable for non-linear systems. Furthermore, almost all of the real-world applications have been encountered with input variance constraints. These constraints limit controllers’ abilities in decreasing the output variability. Therefore, existing MVLB computation methods, which do not account for input constraints, are not realistic when applied to constrained systems. The authors propose a novel approach to estimate MVLB by employing properties of dual Lagrangian functions to address these issues simultaneously in this study. Furthermore, to design the constrained non-linear MV controller (MVC), they propose to use the recurrent neural network for accommodating non-linearities and the input constraints. Then, control loop stability, optimality with respect to MVLB as well as the global convergence of the proposed controller are analytically proved for convex-non-linear systems with input constraints. The proposed control strategy is verified through simulations performed on a non-linear quadruple-tank system. The results indicate that the proposed design provides satisfactory results in decreasing output variance while satisfying the constraints.<br class="zbmathjax-paragraph">© 2021 The Authors. IET Control Theory & Applications published by John Wiley & Sons, Ltd. on behalf of The Institution of Engineering and Technology</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7980544">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anonlinear+control+systems">nonlinear control systems</a>; <a href="/?q=ut%3Acontrol+system+synthesis">control system synthesis</a>; <a href="/?q=ut%3Alinear+systems">linear systems</a>; <a href="/?q=ut%3Aneurocontrollers">neurocontrollers</a>; <a href="/?q=ut%3Arecurrent+neural+nets">recurrent neural nets</a>; <a href="/?q=ut%3Astability">stability</a>; <a href="/?q=ut%3Astochastic+systems">stochastic systems</a>; <a href="/?q=ut%3Aconvergence">convergence</a>; <a href="/?q=ut%3AMV+lower+bound+controller">MV lower bound controller</a>; <a href="/?q=ut%3Aconvex-nonlinear+systems">convex-nonlinear systems</a>; <a href="/?q=ut%3Acontrol+loop+performance">control loop performance</a>; <a href="/?q=ut%3Aminimum+variance+MV+benchmark">minimum variance MV benchmark</a>; <a href="/?q=ut%3Aoptimal+performance+quantification">optimal performance quantification</a>; <a href="/?q=ut%3Aoutput+variance+constraint">output variance constraint</a>; <a href="/?q=ut%3Astochastic+disturbance">stochastic disturbance</a>; <a href="/?q=ut%3Alinear+systems">linear systems</a>; <a href="/?q=ut%3Acontroller+performance+assessment+methods">controller performance assessment methods</a>; <a href="/?q=ut%3Ainput+variance+constraints">input variance constraints</a>; <a href="/?q=ut%3Asaturation+function">saturation function</a>; <a href="/?q=ut%3Anonlinear+quadruple-tank+system">nonlinear quadruple-tank system</a>; <a href="/?q=ut%3Aglobal+convergence">global convergence</a>; <a href="/?q=ut%3Acontrol+loop+stability">control loop stability</a>; <a href="/?q=ut%3Arecurrent+neural+network">recurrent neural network</a>; <a href="/?q=ut%3Aconstrained+nonlinear+MV+controller+design">constrained nonlinear MV controller design</a>; <a href="/?q=ut%3Adual+Lagrangian+functions">dual Lagrangian functions</a>; <a href="/?q=ut%3AMVLB+computation+methods">MVLB computation methods</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 07980544" data-ciurl="/ci/07980544" data-biburl="/bibtex/07980544.bib" data-amsurl="/amsrefs/07980544.bib" data-xmlurl="/xml/07980544.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07980544.pdf" title="Zbl 07980544 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/10.1049/iet-cta.2017.0760" aria-label="DOI for “MV bound and MV controller for convex-non-linear systems with input constraints”" title="10.1049/iet-cta.2017.0760">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">Huang, B.; Shah, S. 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