Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes

Armin Lederer; Sandra Hirche

doi:10.1109/CDC40024.2019.9029489

Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes

Armin Lederer
, Sandra Hirche

Chair of Information-oriented Control

Technical University of Munich

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

14 Scopus citations

Abstract

Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to char-acterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1766-1771
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029489
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	11/12/19 → 13/12/19

Access to Document

10.1109/CDC40024.2019.9029489

Cite this

Lederer, A., & Hirche, S. (2019). Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 1766-1771). Article 9029489 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029489

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title = "Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes",

abstract = "Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to char-acterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.",

author = "Armin Lederer and Sandra Hirche",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/CDC40024.2019.9029489",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Lederer, A & Hirche, S 2019, Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029489, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 1766-1771, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 11/12/19. https://doi.org/10.1109/CDC40024.2019.9029489

Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes. / Lederer, Armin; Hirche, Sandra.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1766-1771 9029489 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

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

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PY - 2019/12

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N2 - Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to char-acterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.

AB - Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to char-acterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.

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U2 - 10.1109/CDC40024.2019.9029489

DO - 10.1109/CDC40024.2019.9029489

M3 - Conference contribution

AN - SCOPUS:85082476918

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1766

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BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

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T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -

Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes

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