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

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

1 Citation (Scopus)

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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
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	3922-3927
Number of pages	6
Volume	2018-December
ISBN (Electronic)	9781538613955
ISBN (Print)	9781538613962
DOIs	https://doi.org/10.1109/CDC.2018.8619669
Publication status	Published - 21 Jan 2019
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name
ISSN (Print)	0743-1546

Conference

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

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10.1109/CDC.2018.8619669

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@inproceedings{f1a8eb33629b4361a48a83e2941e0563,

title = "Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints",

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.",

author = "Andrea Iannelli and Peter Seiler and Andres Marcos",

year = "2019",

month = jan,

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doi = "10.1109/CDC.2018.8619669",

language = "English",

isbn = "9781538613962",

volume = "2018-December",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

pages = "3922--3927",

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address = "United States",

note = "57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

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Iannelli, A, Seiler, P & 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. vol. 2018-December, 8619669, Institute of Electrical and Electronics Engineers (IEEE), pp. 3922-3927, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. 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. Vol. 2018-December Institute of Electrical and Electronics Engineers (IEEE), 2019. p. 3922-3927 8619669.

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints

AU - Iannelli, Andrea

AU - Seiler, Peter

AU - Marcos, Andres

PY - 2019/1/21

Y1 - 2019/1/21

N2 - 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.

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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U2 - 10.1109/CDC.2018.8619669

DO - 10.1109/CDC.2018.8619669

M3 - Conference Contribution (Conference Proceeding)

AN - SCOPUS:85062177293

SN - 9781538613962

VL - 2018-December

SP - 3922

EP - 3927

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers (IEEE)

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -

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

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