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Article: LMI techniques for optimization over polynomials in control: A survey

TitleLMI techniques for optimization over polynomials in control: A survey
Authors
KeywordsControl system
linear matrix inequality (LMI)
optimization
polynomial
positivity
Issue Date2010
PublisherIEEE.
Citation
Ieee Transactions On Automatic Control, 2010, v. 55 n. 11, p. 2500-2510 How to Cite?
AbstractNumerous tasks in control systems involve optimization problems over polynomials, and unfortunately these problems are in general nonconvex. In order to cope with this difficulty, linear matrix inequality (LMI) techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems. This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Plya's theorem, and matrix dilation. Moreover, it aims to provide a collection of the essential problems in control systems where these LMI techniques are used, such as stability and performance investigations in nonlinear systems, uncertain systems, time-delay systems, and genetic regulatory networks. It is expected that this survey may be a concise useful reference for all readers. © 2006 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/135115
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
ISI Accession Number ID
Funding AgencyGrant Number
Research Grants Council of Hong KongHKU711208E
Funding Information:

Manuscript received July 14, 2008; revised July 07, 2009; accepted March 15, 2010. First published April 05, 2010; current version published November 03, 2010. This work was supported in part by the Research Grants Council of Hong Kong (HKU711208E). Recommended by Associate Editor P. Parrilo.

References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2011-07-27T01:28:29Z-
dc.date.available2011-07-27T01:28:29Z-
dc.date.issued2010en_HK
dc.identifier.citationIeee Transactions On Automatic Control, 2010, v. 55 n. 11, p. 2500-2510en_HK
dc.identifier.issn0018-9286en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135115-
dc.description.abstractNumerous tasks in control systems involve optimization problems over polynomials, and unfortunately these problems are in general nonconvex. In order to cope with this difficulty, linear matrix inequality (LMI) techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems. This survey aims to provide the reader with a significant overview of the LMI techniques that are used in control systems for tackling optimization problems over polynomials, describing approaches such as decomposition in sum of squares, Positivstellensatz, theory of moments, Plya's theorem, and matrix dilation. Moreover, it aims to provide a collection of the essential problems in control systems where these LMI techniques are used, such as stability and performance investigations in nonlinear systems, uncertain systems, time-delay systems, and genetic regulatory networks. It is expected that this survey may be a concise useful reference for all readers. © 2006 IEEE.en_HK
dc.languageengen_US
dc.publisherIEEE.-
dc.relation.ispartofIEEE Transactions on Automatic Controlen_HK
dc.rightsIEEE Transactions on Automatic Control. Copyright © IEEE.-
dc.rights©2010 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.subjectControl systemen_HK
dc.subjectlinear matrix inequality (LMI)en_HK
dc.subjectoptimizationen_HK
dc.subjectpolynomialen_HK
dc.subjectpositivityen_HK
dc.titleLMI techniques for optimization over polynomials in control: A surveyen_HK
dc.typeArticleen_HK
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/TAC.2010.2046926en_HK
dc.identifier.scopuseid_2-s2.0-77957703812en_HK
dc.identifier.hkuros187528en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77957703812&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume55en_HK
dc.identifier.issue11en_HK
dc.identifier.spage2500en_HK
dc.identifier.epage2510en_HK
dc.identifier.isiWOS:000283940800005-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK
dc.identifier.citeulike8208593-

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