A new algorithm for L2 optimal model reduction
In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal...
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Veröffentlicht in: | Automatica (Oxford) 1992-09, Vol.28 (5), p.897-909 |
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creator | Spanos, J.T. Milman, M.H. Mingori, D.L. |
description | In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm. |
doi_str_mv | 10.1016/0005-1098(92)90143-4 |
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The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.</description><identifier>ISSN: 0005-1098</identifier><identifier>EISSN: 1873-2836</identifier><identifier>DOI: 10.1016/0005-1098(92)90143-4</identifier><identifier>CODEN: ATCAA9</identifier><language>eng</language><publisher>Legacy CDMS: Elsevier Ltd</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Control theory. Systems ; Cybernetics ; Exact sciences and technology ; least-squares approximations ; Model reduction ; Optimal control ; optimization</subject><ispartof>Automatica (Oxford), 1992-09, Vol.28 (5), p.897-909</ispartof><rights>1992</rights><rights>1992 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c451t-30e070007d9c64219edc78ee22e5642a94d251fa8b01c171dd06cd8e9bd42503</citedby><cites>FETCH-LOGICAL-c451t-30e070007d9c64219edc78ee22e5642a94d251fa8b01c171dd06cd8e9bd42503</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/0005-1098(92)90143-4$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5498363$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Spanos, J.T.</creatorcontrib><creatorcontrib>Milman, M.H.</creatorcontrib><creatorcontrib>Mingori, D.L.</creatorcontrib><title>A new algorithm for L2 optimal model reduction</title><title>Automatica (Oxford)</title><description>In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control theory. Systems</subject><subject>Cybernetics</subject><subject>Exact sciences and technology</subject><subject>least-squares approximations</subject><subject>Model reduction</subject><subject>Optimal control</subject><subject>optimization</subject><issn>0005-1098</issn><issn>1873-2836</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><sourceid>CYI</sourceid><recordid>eNp9kE9PwzAMxSMEEmPwDXboASE4dDhp2iYXJDTxT5rEZfcoS1wIapuRdCC-PRmdduRkPfln-_kRMqMwp0CrWwAocwpSXEt2I4HyIudHZEJFXeRMFNUxmRyQU3IW40eSnAo2IfP7rMfvTLdvPrjhvcsaH7Ily_xmcJ1us85bbLOAdmsG5_tzctLoNuLFvk7J6vFhtXjOl69PL4v7ZW54SYe8AIQ63aitNBVnVKI1tUBkDMukteSWlbTRYg3U0JpaC5WxAuXaclZCMSVX49pN8J9bjIPqXDTYtrpHv42KlbVgwFkC-Qia4GMM2KhNSL7Dj6Kgdtmo3eNq97iSTP1lo3gau9zv19Hotgm6Ny4eZksuU2pFwmYj1uuoVT-EqKiUBUAhoJKpfTe2MSXx5TCoaBz2Bq0LaAZlvfvfxi8JBn22</recordid><startdate>19920901</startdate><enddate>19920901</enddate><creator>Spanos, J.T.</creator><creator>Milman, M.H.</creator><creator>Mingori, D.L.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>CYE</scope><scope>CYI</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>19920901</creationdate><title>A new algorithm for L2 optimal model reduction</title><author>Spanos, J.T. ; Milman, M.H. ; Mingori, D.L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c451t-30e070007d9c64219edc78ee22e5642a94d251fa8b01c171dd06cd8e9bd42503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Control theory. Systems</topic><topic>Cybernetics</topic><topic>Exact sciences and technology</topic><topic>least-squares approximations</topic><topic>Model reduction</topic><topic>Optimal control</topic><topic>optimization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Spanos, J.T.</creatorcontrib><creatorcontrib>Milman, M.H.</creatorcontrib><creatorcontrib>Mingori, D.L.</creatorcontrib><collection>NASA Scientific and Technical Information</collection><collection>NASA Technical Reports Server</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Automatica (Oxford)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Spanos, J.T.</au><au>Milman, M.H.</au><au>Mingori, D.L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new algorithm for L2 optimal model reduction</atitle><jtitle>Automatica (Oxford)</jtitle><date>1992-09-01</date><risdate>1992</risdate><volume>28</volume><issue>5</issue><spage>897</spage><epage>909</epage><pages>897-909</pages><issn>0005-1098</issn><eissn>1873-2836</eissn><coden>ATCAA9</coden><abstract>In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.</abstract><cop>Legacy CDMS</cop><pub>Elsevier Ltd</pub><doi>10.1016/0005-1098(92)90143-4</doi><tpages>13</tpages></addata></record> |
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subjects | Applied sciences Computer science control theory systems Control theory. Systems Cybernetics Exact sciences and technology least-squares approximations Model reduction Optimal control optimization |
title | A new algorithm for L2 optimal model reduction |
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