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Article: An approximate approach to H 2 optimal model reduction

TitleAn approximate approach to H 2 optimal model reduction
Authors
KeywordsLinear systems
Model reduction
Optimization
System approximation
Issue Date1999
PublisherIEEE.
Citation
Ieee Transactions On Automatic Control, 1999, v. 44 n. 7, p. 1341-1358 How to Cite?
AbstractThis paper deals with the problem of computing an H 2 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 H 2 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 expression for the gradient of the cost over the manifold is derived, from which a gradient flow results as an ordinary differential equation (ODE). A number of nice properties about such a flow are established. Furthermore, two explicit iterative convergent algorithms are developed from the flow; one has a constant step-size and the other has a varying step-size and is much more efficient. Both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates. A procedure for closing the gap between the original and modified problem is proposed. In the symmetric case, the two problems are shown to be equivalent. Numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence.
Persistent Identifierhttp://hdl.handle.net/10722/43029
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
References

 

DC FieldValueLanguage
dc.contributor.authorYan, WYen_HK
dc.contributor.authorLam, Jen_HK
dc.date.accessioned2007-03-23T04:37:13Z-
dc.date.available2007-03-23T04:37:13Z-
dc.date.issued1999en_HK
dc.identifier.citationIeee Transactions On Automatic Control, 1999, v. 44 n. 7, p. 1341-1358en_HK
dc.identifier.issn0018-9286en_HK
dc.identifier.urihttp://hdl.handle.net/10722/43029-
dc.description.abstractThis paper deals with the problem of computing an H 2 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 H 2 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 expression for the gradient of the cost over the manifold is derived, from which a gradient flow results as an ordinary differential equation (ODE). A number of nice properties about such a flow are established. Furthermore, two explicit iterative convergent algorithms are developed from the flow; one has a constant step-size and the other has a varying step-size and is much more efficient. Both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates. A procedure for closing the gap between the original and modified problem is proposed. In the symmetric case, the two problems are shown to be equivalent. Numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence.en_HK
dc.format.extent448549 bytes-
dc.format.extent35328 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.languageengen_HK
dc.publisherIEEE.en_HK
dc.relation.ispartofIEEE Transactions on Automatic Controlen_HK
dc.rights©1999 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.subjectLinear systemsen_HK
dc.subjectModel reductionen_HK
dc.subjectOptimizationen_HK
dc.subjectSystem approximationen_HK
dc.titleAn approximate approach to H 2 optimal model reductionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0018-9286&volume=44&issue=7&spage=1341&epage=1358&date=1999&atitle=An+approximate+approach+to+H2+optimal+model+reductionen_HK
dc.identifier.emailLam, J:james.lam@hku.hken_HK
dc.identifier.authorityLam, J=rp00133en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/9.774107en_HK
dc.identifier.scopuseid_2-s2.0-0032666654en_HK
dc.identifier.hkuros51701-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032666654&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume44en_HK
dc.identifier.issue7en_HK
dc.identifier.spage1341en_HK
dc.identifier.epage1358en_HK
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridYan, WY=7402221751en_HK
dc.identifier.scopusauthoridLam, J=7201973414en_HK

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