Document Zbl 1425.93284

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J. Adapt. Control Signal Process.</a> <a href="/?q=in%3A436107" title="Articles in this Issue">33, No. 7, 1189-1211 (2019)</a>. </div> <div class="abstract">Summary: For a special class of nonlinear systems (i.e., bilinear systems) with autoregressive moving average noise, this paper gives the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering-based maximum likelihood hierarchical gradient iterative algorithm and a filtering-based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient-based iterative algorithm and the multi-innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7124148">Cited in <strong>98</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93E11" title="MSC2020">93E11</a> </td> <td class="space"> Filtering in stochastic control theory </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%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%3Abilinear+system">bilinear system</a>; <a href="/?q=ut%3Ahierarchical+principle">hierarchical principle</a>; <a href="/?q=ut%3Aiterative+identification">iterative identification</a>; <a href="/?q=ut%3Amaximum+likelihood">maximum likelihood</a>; <a href="/?q=ut%3Aparameter+estimation">parameter 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 1425.93284" data-ciurl="/ci/07124148" data-biburl="/bibtex/07124148.bib" data-amsurl="/amsrefs/07124148.bib" data-xmlurl="/xml/07124148.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07124148.pdf" title="Zbl 1425.93284 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/10.1002/acs.3029" aria-label="DOI for “The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle”" title="10.1002/acs.3029">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">Gan, M.; 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