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Conference Paper: L2 optimal model reduction

TitleL2 optimal model reduction
Authors
KeywordsTechnology: comprehensive works
Issue Date1996
PublisherIEEE. The Journal's web site is located at http://www.ieeecss.org
Citation
Proceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281 How to Cite?
Abstract
This paper deals with the problem of computing an L2-optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the L2 model reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form formula for the gradient of the cost over the manifold is derived, from which a gradient flow is formed as an ordinary differential equation. A number of nice properties about such a flow are obtained. Among them are the decreasing property of the cost along the ODE solution and the convergence of the flow from any starting point in the manifold. Furthermore, an explicit iterative convergent algorithm is developed from the flow and inherits the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model-reduction cost is decreasing to minimums along the iterates.
Persistent Identifierhttp://hdl.handle.net/10722/46622
ISSN
2013 SCImago Journal Rankings: 0.400

 

Author Affiliations
  1. Nanyang Technological University
DC FieldValueLanguage
dc.contributor.authorYan, WeiYongen_HK
dc.contributor.authorLam, Jamesen_HK
dc.date.accessioned2007-10-30T06:54:27Z-
dc.date.available2007-10-30T06:54:27Z-
dc.date.issued1996en_HK
dc.identifier.citationProceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281en_HK
dc.identifier.issn0191-2216en_HK
dc.identifier.urihttp://hdl.handle.net/10722/46622-
dc.description.abstractThis paper deals with the problem of computing an L2-optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the L2 model reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form formula for the gradient of the cost over the manifold is derived, from which a gradient flow is formed as an ordinary differential equation. A number of nice properties about such a flow are obtained. Among them are the decreasing property of the cost along the ODE solution and the convergence of the flow from any starting point in the manifold. Furthermore, an explicit iterative convergent algorithm is developed from the flow and inherits the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model-reduction cost is decreasing to minimums along the iterates.en_HK
dc.format.extent557762 bytes-
dc.format.extent10566 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherIEEE. The Journal's web site is located at http://www.ieeecss.orgen_HK
dc.relation.ispartofProceedings of the IEEE Conference on Decision and Controlen_HK
dc.rights©1996 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectTechnology: comprehensive worksen_HK
dc.titleL2 optimal model reductionen_HK
dc.typeConference_Paperen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0743-1546&volume=4&spage=4276&epage=4281&date=1996&atitle=L2+optimal+model+reductionen_HK
dc.identifier.emailLam, James:james.lam@hku.hken_HK
dc.identifier.authorityLam, James=rp00133en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/CDC.1996.577460en_HK
dc.identifier.scopuseid_2-s2.0-0030385488en_HK
dc.identifier.hkuros25686-
dc.identifier.volume4en_HK
dc.identifier.spage4276en_HK
dc.identifier.epage4281en_HK
dc.identifier.scopusauthoridYan, WeiYong=7402221751en_HK
dc.identifier.scopusauthoridLam, James=7201973414en_HK

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