Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints

Andrea Iannelli; Peter Seiler; Andres Marcos

doi:10.1109/CDC.2018.8619669

Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints

Andrea Iannelli, Peter Seiler, Andres Marcos

Aerospace Engineering and Mechanics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

Original language	English (US)
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3922-3927
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619669
State	Published - Jul 2 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	12/17/18 → 12/19/18

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Publisher Copyright:
© 2018 IEEE.

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10.1109/CDC.2018.8619669

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Iannelli, A., Seiler, P., & Marcos, A. (2018). Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3922-3927). Article 8619669 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619669

Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints. / Iannelli, Andrea; Seiler, Peter; Marcos, Andres.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 3922-3927 8619669 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Iannelli, A, Seiler, P & Marcos, A 2018, Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619669, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 3922-3927, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619669

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AB - A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

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Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints

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