An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Simone Baldi

doi:10.1109/CDC.2016.7798857

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

^*Corresponding author for this work

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

90 Downloads (Pure)

Abstract

This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-of-Squares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

Original language	English
Title of host publication	Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC)
Editors	Francesco Bullo, Christophe Prieur, Alessandro Giua
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	3892-3897
ISBN (Electronic)	978-1-5090-1837-6
DOIs	https://doi.org/10.1109/CDC.2016.7798857
Publication status	Published - 2016
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016

Conference

Conference	55th IEEE Conference on Decision and Control, CDC 2016
Abbreviated title	CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 14/12/16

Bibliographical note

Accepted Author Manuscript

Keywords

Output feedback
Optimization
Nonlinear systems
Iterative methods
Convergence
Lyapunov methods
Symmetric matrices

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10.1109/CDC.2016.7798857

SOS_resub_CDC_finalAccepted author manuscript, 165 KB

Cite this

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title = "An iterative Sum-of-Squares optimization for static output feedback of polynomial systems",

abstract = "This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-of-Squares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.",

keywords = "Output feedback, Optimization, Nonlinear systems, Iterative methods, Convergence, Lyapunov methods, Symmetric matrices",

author = "Simone Baldi",

note = "Accepted Author Manuscript; 55th IEEE Conference on Decision and Control, CDC 2016, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

year = "2016",

doi = "10.1109/CDC.2016.7798857",

language = "English",

pages = "3892--3897",

editor = "Francesco Bullo and Christophe Prieur and Giua, {Alessandro }",

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address = "United States",

}

Baldi, S 2016, An iterative Sum-of-Squares optimization for static output feedback of polynomial systems. in F Bullo, C Prieur & A Giua (eds), Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC) ., 7798857, IEEE, Piscataway, NJ, USA, pp. 3892-3897, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7798857

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems. / Baldi, Simone.
Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC) . ed. / Francesco Bullo; Christophe Prieur; Alessandro Giua. Piscataway, NJ, USA: IEEE, 2016. p. 3892-3897 7798857.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AB - This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-of-Squares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

KW - Output feedback

KW - Optimization

KW - Nonlinear systems

KW - Iterative methods

KW - Convergence

KW - Lyapunov methods

KW - Symmetric matrices

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EP - 3897

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A2 - Prieur, Christophe

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T2 - 55th IEEE Conference on Decision and Control, CDC 2016

Y2 - 12 December 2016 through 14 December 2016

ER -

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

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Keywords

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