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Article: LMI techniques for optimization over polynomials in control: A survey
Title | LMI techniques for optimization over polynomials in control: A survey | ||||
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Authors | |||||
Keywords | Control system linear matrix inequality (LMI) optimization polynomial positivity | ||||
Issue Date | 2010 | ||||
Publisher | IEEE. | ||||
Citation | Ieee Transactions On Automatic Control, 2010, v. 55 n. 11, p. 2500-2510 How to Cite? | ||||
Abstract | Numerous 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 Identifier | http://hdl.handle.net/10722/135115 | ||||
ISSN | 2023 Impact Factor: 6.2 2023 SCImago Journal Rankings: 4.501 | ||||
ISI Accession Number ID |
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 Field | Value | Language |
---|---|---|
dc.contributor.author | Chesi, G | en_HK |
dc.date.accessioned | 2011-07-27T01:28:29Z | - |
dc.date.available | 2011-07-27T01:28:29Z | - |
dc.date.issued | 2010 | en_HK |
dc.identifier.citation | Ieee Transactions On Automatic Control, 2010, v. 55 n. 11, p. 2500-2510 | en_HK |
dc.identifier.issn | 0018-9286 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/135115 | - |
dc.description.abstract | Numerous 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.language | eng | en_US |
dc.publisher | IEEE. | - |
dc.relation.ispartof | IEEE Transactions on Automatic Control | en_HK |
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.subject | Control system | en_HK |
dc.subject | linear matrix inequality (LMI) | en_HK |
dc.subject | optimization | en_HK |
dc.subject | polynomial | en_HK |
dc.subject | positivity | en_HK |
dc.title | LMI techniques for optimization over polynomials in control: A survey | en_HK |
dc.type | Article | en_HK |
dc.identifier.email | Chesi, G:chesi@eee.hku.hk | en_HK |
dc.identifier.authority | Chesi, G=rp00100 | en_HK |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1109/TAC.2010.2046926 | en_HK |
dc.identifier.scopus | eid_2-s2.0-77957703812 | en_HK |
dc.identifier.hkuros | 187528 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-77957703812&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 55 | en_HK |
dc.identifier.issue | 11 | en_HK |
dc.identifier.spage | 2500 | en_HK |
dc.identifier.epage | 2510 | en_HK |
dc.identifier.isi | WOS:000283940800005 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Chesi, G=7006328614 | en_HK |
dc.identifier.citeulike | 8208593 | - |
dc.identifier.issnl | 0018-9286 | - |