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Article: On the complexity of SOS programming and applications in control systems
Title | On the complexity of SOS programming and applications in control systems |
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Authors | |
Keywords | SOS LMI control system domain of attraction robust stability |
Issue Date | 2018 |
Publisher | Wiley-Blackwell Publishing, Inc. & Chinese Automatic Control Society. The Journal's web site is located at http://www.wiley.com/bw/journal.asp?ref=1561-8625 |
Citation | Asian Journal of Control, 2018, v. 20 n. 5, p. 2005-2013 How to Cite? |
Abstract | The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed for real and complex matrix polynomials, in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. Two applications in control systems are presented in order to show the usefulness of the proposed results. |
Persistent Identifier | http://hdl.handle.net/10722/272178 |
ISSN | 2023 Impact Factor: 2.7 2023 SCImago Journal Rankings: 0.677 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chesi, G | - |
dc.date.accessioned | 2019-07-20T10:37:12Z | - |
dc.date.available | 2019-07-20T10:37:12Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Asian Journal of Control, 2018, v. 20 n. 5, p. 2005-2013 | - |
dc.identifier.issn | 1561-8625 | - |
dc.identifier.uri | http://hdl.handle.net/10722/272178 | - |
dc.description.abstract | The minimization of a linear cost function subject to the condition that some matrix polynomials depending linearly on the decision variables are sums of squares of matrix polynomials (SOS) is known as SOS programming. This paper proposes an analysis of the complexity of SOS programming, in particular of the number of linear matrix inequality (LMI) scalar variables required for establishing whether a matrix polynomial is SOS. This number is analyzed for real and complex matrix polynomials, in the general case and in the case of some exact reductions achievable for some classes of matrix polynomials. An analytical formula is proposed in each case in order to provide this number as a function of the number of variables, degree and size of the matrix polynomials. Some tables reporting this number are also provided as reference for the reader. Two applications in control systems are presented in order to show the usefulness of the proposed results. | - |
dc.language | eng | - |
dc.publisher | Wiley-Blackwell Publishing, Inc. & Chinese Automatic Control Society. The Journal's web site is located at http://www.wiley.com/bw/journal.asp?ref=1561-8625 | - |
dc.relation.ispartof | Asian Journal of Control | - |
dc.rights | Preprint This is the pre-peer reviewed version of the following article: [FULL CITE], which has been published in final form at [Link to final article using the DOI]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. Postprint This is the peer reviewed version of the following article: [FULL CITE], which has been published in final form at [Link to final article using the DOI]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. | - |
dc.subject | SOS | - |
dc.subject | LMI | - |
dc.subject | control system | - |
dc.subject | domain of attraction | - |
dc.subject | robust stability | - |
dc.title | On the complexity of SOS programming and applications in control systems | - |
dc.type | Article | - |
dc.identifier.email | Chesi, G: chesi@eee.hku.hk | - |
dc.identifier.authority | Chesi, G=rp00100 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/asjc.1684 | - |
dc.identifier.scopus | eid_2-s2.0-85035091177 | - |
dc.identifier.hkuros | 299104 | - |
dc.identifier.volume | 20 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 2005 | - |
dc.identifier.epage | 2013 | - |
dc.identifier.isi | WOS:000445600400026 | - |
dc.publisher.place | Taiwan | - |
dc.identifier.issnl | 1561-8625 | - |