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Conference Paper: L2 optimal model reduction
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TitleL2 optimal model reduction
 
AuthorsYan, WeiYong1
Lam, James1
 
KeywordsTechnology: comprehensive works
 
Issue Date1996
 
PublisherIEEE. The Journal's web site is located at http://www.ieeecss.org
 
CitationProceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281 [How to Cite?]
DOI: http://dx.doi.org/10.1109/CDC.1996.577460
 
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.
 
ISSN0191-2216
2012 SCImago Journal Rankings: 0.746
 
DOIhttp://dx.doi.org/10.1109/CDC.1996.577460
 
DC FieldValue
dc.contributor.authorYan, WeiYong
 
dc.contributor.authorLam, James
 
dc.date.accessioned2007-10-30T06:54:27Z
 
dc.date.available2007-10-30T06:54:27Z
 
dc.date.issued1996
 
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.
 
dc.description.naturepublished_or_final_version
 
dc.format.extent557762 bytes
 
dc.format.extent10566 bytes
 
dc.format.mimetypeapplication/pdf
 
dc.format.mimetypetext/plain
 
dc.identifier.citationProceedings Of The Ieee Conference On Decision And Control, 1996, v. 4, p. 4276-4281 [How to Cite?]
DOI: http://dx.doi.org/10.1109/CDC.1996.577460
 
dc.identifier.doihttp://dx.doi.org/10.1109/CDC.1996.577460
 
dc.identifier.epage4281
 
dc.identifier.hkuros25686
 
dc.identifier.issn0191-2216
2012 SCImago Journal Rankings: 0.746
 
dc.identifier.openurl
 
dc.identifier.scopuseid_2-s2.0-0030385488
 
dc.identifier.spage4276
 
dc.identifier.urihttp://hdl.handle.net/10722/46622
 
dc.identifier.volume4
 
dc.languageeng
 
dc.publisherIEEE. The Journal's web site is located at http://www.ieeecss.org
 
dc.relation.ispartofProceedings of the IEEE Conference on Decision and Control
 
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.
 
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License
 
dc.subjectTechnology: comprehensive works
 
dc.titleL2 optimal model reduction
 
dc.typeConference_Paper
 
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Author Affiliations
  1. Nanyang Technological University