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

Andrea Iannelli, Peter J Seiler Jr, Andres Marcos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3922-3927
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Quadratic Constraint
Uncertain systems
Uncertain Systems
Polynomials
Polynomial Vector Fields
Sum of squares
Bounded Operator
Factorization
Closed loop systems
Interconnection
Iterative Algorithm
Closed-loop System
Mathematical operators
Nonlinear Systems
Nonlinearity
Feedback
Uncertainty
Numerical Examples
Polynomial
Optimization

Cite this

Iannelli, A., Seiler Jr, P. J., & Marcos, A. (2019). 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). [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 Jr, Peter J; Marcos, Andres.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 3922-3927 8619669 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Iannelli, A, Seiler Jr, PJ & Marcos, A 2019, 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
Iannelli A, Seiler Jr PJ, Marcos A. Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 3922-3927. 8619669. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619669
Iannelli, Andrea ; Seiler Jr, Peter J ; Marcos, Andres. / Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 3922-3927 (Proceedings of the IEEE Conference on Decision and Control).
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