Document Zbl 1538.93020

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English summary)</i> <a class="label nowrap" href="/1538.93020">Zbl 1538.93020</a> </h2> <div class="source"> <a href="/serials/8628" title="Journal Profile">Zh. Sredn. Mat. Obshch.</a> <a href="/?q=in%3A507409" title="Articles in this Issue">21, No. 4, 469-479 (2019)</a>. </div> <div class="abstract">Summary: The paper addresses the problem of dynamic identification of mixed boundary conditions for one-dimensional convection-diffusion transport model based on noisy measurements of the function of interest. Using finite difference method the original model with the partial differential equation is replaced with the discrete linear dynamic system with noisy multisensor measurements in which boundary conditions are included as unknown input vector. To solve the problem, the algorithm of simultaneous estimation of the state and input vectors is used. The results of numerical experiments are presented which confirm the practical applicability of the proposed method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7794051">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%3A93C20" title="MSC2020">93C20</a> </td> <td class="space"> Control/observation systems governed by partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E12" title="MSC2020">93E12</a> </td> <td class="space"> Identification in stochastic control theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C55" title="MSC2020">93C55</a> </td> <td class="space"> Discrete-time control/observation systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apartial+differential+equations">partial differential equations</a>; <a href="/?q=ut%3Aboundary+problems">boundary problems</a>; <a href="/?q=ut%3Adiscrete+linear+stochastic+system">discrete linear stochastic system</a>; <a href="/?q=ut%3Aparameter+identification">parameter identification</a>; <a href="/?q=ut%3Aoptimal+estimation">optimal estimation</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 1538.93020" data-ciurl="/ci/07794051" data-biburl="/bibtex/07794051.bib" data-amsurl="/amsrefs/07794051.bib" data-xmlurl="/xml/07794051.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07794051.pdf" title="Zbl 1538.93020 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/10.15507/2079-6900.21.201904.469-479" aria-label="DOI for “Dynamic identification of boundary conditions for convection-diffusion transport model in the case of noisy measurements”" title="10.15507/2079-6900.21.201904.469-479">DOI</a> <a class="btn btn-default btn-xs" type="button" href="http://mathnet.ru/eng/svmo754" title="Math-Net.Ru">MNR</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. M. Denisov, Introduction to the theory of inverse problems, Studies. benefit, Publishing House of Moscow State University, Moscow, 1994, 208 pp. (In Russ.)</td> </tr><tr> <td>[2]</td> <td class="space">A. I. Leontyev, Theory of heat and mass transfer, studies. for machine building. spets. Techn. universities and higher education institutions, MGTU, Moscow, 1997, 683 pp. (In Russ.)</td> </tr><tr> <td>[3]</td> <td class="space">S. Farlou, Partial differential equations for scientists and engineers, Mir, Moscow, 1985, 384 pp. (In Russ.) · <a href="/0673.35001" class="nowrap">Zbl 0673.35001</a></td> </tr><tr> <td>[4]</td> <td class="space">S. Gillijns, B. D. Moor, “Joint state and boundary condition estimation in linear data assimilation using basis function expansion”, Proceedings of the 26th IASTED International Conference on Modelling, Identification, and Control (Innsbruck, Austria), 2007, 458-463</td> </tr><tr> <td>[5]</td> <td class="space">A. V. Tsyganov, Yu. V. Tsyganova, A. N. Kuvshinova, H. R. Tapia Garza, “Metaheuristic algorithms for identification of the convection velocity in the convection-diffusion transport model”, Proceedings of the II International Scientific and Practical Conference “Fuzzy Technologies in the Industry - FTI 2018”, 2018, 188-196</td> </tr><tr> <td>[6]</td> <td class="space">A.V. Tsyganov, Yu.V. Tsyganova, A.N. Kuvshinova, “Dynamic identification of boundary conditions for convection-diffusion transport model in the case of noisy measurements”, Proceedings of the V International Conference and Youth School «Information Technologies and Nanotechnologies», New technique, 2019, 169-177 (In Russ.)</td> </tr><tr> <td>[7]</td> <td class="space">S. Gillijns, B. D. Moor, “Unbiased minimum-variance input and state estimation for linear discrete-time systems”, Automatica, 43 (2007), 111-116 · <a href="/1140.93480" class="nowrap">Zbl 1140.93480</a> · <a href="https://doi.org/10.1016/j.automatica.2006.08.002" class="nowrap">doi:10.1016/j.automatica.2006.08.002</a></td> </tr><tr> <td>[8]</td> <td class="space">P. K. Kitanidis, “Unbiased minimum-variance linear state estimation”, Automatica, 23:6 (1987), 775-778 · <a href="/0627.93065" class="nowrap">Zbl 0627.93065</a> · <a href="https://doi.org/10.1016/0005-1098(87)90037-9" class="nowrap">doi:10.1016/0005-1098(87)90037-9</a></td> </tr><tr> <td>[9]</td> <td class="space">M. Darouach, M. Zasadzinski, “Unbiased minimum variance estimation for systems with unknown exogenious inputs”, Automatica, 33:4 (1997), 717-719 · <a href="/0874.93086" class="nowrap">Zbl 0874.93086</a> · <a href="https://doi.org/10.1016/S0005-1098(96)00217-8" class="nowrap">doi:10.1016/S0005-1098(96)00217-8</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 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"> © 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 & 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"> <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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