Conference Paper: L2 optimal model reduction

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Title	L2 optimal model reduction
Authors	Yan, WeiYong1 Lam, James1
Keywords	Technology: comprehensive works
Issue Date	1996
Publisher	IEEE. 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?] DOI: http://dx.doi.org/10.1109/CDC.1996.577460
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.
ISSN	0191-2216 2011 SCImago Journal Rankings: 0.032
DOI	http://dx.doi.org/10.1109/CDC.1996.577460

DC Field	Value
dc.contributor.author	Yan, WeiYong
dc.contributor.author	Lam, James
dc.date.accessioned	2007-10-30T06:54:27Z
dc.date.available	2007-10-30T06:54:27Z
dc.date.issued	1996
dc.description.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.
dc.description.nature	published_or_final_version
dc.format.extent	557762 bytes
dc.format.extent	10566 bytes
dc.format.mimetype	application/pdf
dc.format.mimetype	text/plain
dc.identifier.citation	Proceedings 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.doi	http://dx.doi.org/10.1109/CDC.1996.577460
dc.identifier.epage	4281
dc.identifier.hkuros	25686
dc.identifier.issn	0191-2216 2011 SCImago Journal Rankings: 0.032
dc.identifier.openurl
dc.identifier.scopus	eid_2-s2.0-0030385488
dc.identifier.spage	4276
dc.identifier.uri	http://hdl.handle.net/10722/46622
dc.identifier.volume	4
dc.language	eng
dc.publisher	IEEE. The Journal's web site is located at http://www.ieeecss.org
dc.relation.ispartof	Proceedings 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.rights	Creative Commons: Attribution 3.0 Hong Kong License
dc.subject	Technology: comprehensive works
dc.title	L2 optimal model reduction
dc.type	Conference_Paper

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Author Affiliations

Nanyang Technological University