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Article: Designing parametric linear quadratic regulators for parametric LTI systems via LMIs
Title | Designing parametric linear quadratic regulators for parametric LTI systems via LMIs |
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Authors | |
Keywords | Parametric system Linear quadratic regulator Linear matrix inequality |
Issue Date | 2019 |
Publisher | Taylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.asp |
Citation | International Journal of Control, 2019, v. 92 n. 12, p. 2907-2916 How to Cite? |
Abstract | This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology. |
Persistent Identifier | http://hdl.handle.net/10722/284557 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 0.862 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chesi, G | - |
dc.contributor.author | Shen, T | - |
dc.date.accessioned | 2020-08-07T08:59:19Z | - |
dc.date.available | 2020-08-07T08:59:19Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | International Journal of Control, 2019, v. 92 n. 12, p. 2907-2916 | - |
dc.identifier.issn | 0020-7179 | - |
dc.identifier.uri | http://hdl.handle.net/10722/284557 | - |
dc.description.abstract | This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant systems affected by parameters through rational functions. Three situations are considered, where the sought controller has to minimise the best cost, average cost, and worst cost, respectively, over the set of admissible parameters. It is shown that candidates for such controllers can be obtained by solving convex optimisation problems with linear matrix inequality (LMI) constraints. These candidates are guaranteed to approximate arbitrarily well the sought controllers by sufficiently increasing the size of the LMIs. In particular, the candidate that minimises the average cost approximates arbitrarily well the true LQR over the set of admissible parameters. Moreover, conditions for establishing the optimality of the found candidates are provided. Some numerical examples illustrate the proposed methodology. | - |
dc.language | eng | - |
dc.publisher | Taylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.asp | - |
dc.relation.ispartof | International Journal of Control | - |
dc.rights | This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Control on 26 Apr 2018, available online: http://www.tandfonline.com/10.1080/00207179.2018.1466058 | - |
dc.subject | Parametric system | - |
dc.subject | Linear quadratic regulator | - |
dc.subject | Linear matrix inequality | - |
dc.title | Designing parametric linear quadratic regulators for parametric LTI systems via LMIs | - |
dc.type | Article | - |
dc.identifier.email | Chesi, G: chesi@eee.hku.hk | - |
dc.identifier.authority | Chesi, G=rp00100 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1080/00207179.2018.1466058 | - |
dc.identifier.scopus | eid_2-s2.0-85046016698 | - |
dc.identifier.hkuros | 312352 | - |
dc.identifier.volume | 92 | - |
dc.identifier.issue | 12 | - |
dc.identifier.spage | 2907 | - |
dc.identifier.epage | 2916 | - |
dc.identifier.isi | WOS:000487014200015 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0020-7179 | - |