Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems

Brendon K. Colbert; Matthew Peet

doi:10.1109/CDC.2018.8618959

Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems

Brendon K. Colbert, Matthew Peet

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

5 Scopus citations

Abstract

We propose a method to estimate the region of attraction of a nonlinear ODE based only on measurements of the trajectory - implying that the nonlinear vector field need not be known a priori. This method is based on using trajectory data to determine values of a form of converse Lyapunov function at a finite number of points in the state-space. Least absolute deviations is then used to fit this data to a Sum-of-Squares polynomial whose level sets then become estimates for the region of attraction. This learned Lyapunov function can then be used to predict whether newly generated initial conditions lie in the region of attraction. Extensive numerical testing is used to show that the method correctly predicts whether a new initial condition is within the region of attraction of the nonlinear ODE on over 95% of a generated set of test data.

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	2341-2347
Number of pages	7
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8618959
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

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2018.8618959

Cite this

Colbert, B. K., & Peet, M. (2018). Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 2341-2347). [8618959] (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.2018.8618959

Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems. / Colbert, Brendon K.; Peet, Matthew.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2341-2347 8618959 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

Colbert, BK & Peet, M 2018, Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618959, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 2341-2347, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8618959

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abstract = "We propose a method to estimate the region of attraction of a nonlinear ODE based only on measurements of the trajectory - implying that the nonlinear vector field need not be known a priori. This method is based on using trajectory data to determine values of a form of converse Lyapunov function at a finite number of points in the state-space. Least absolute deviations is then used to fit this data to a Sum-of-Squares polynomial whose level sets then become estimates for the region of attraction. This learned Lyapunov function can then be used to predict whether newly generated initial conditions lie in the region of attraction. Extensive numerical testing is used to show that the method correctly predicts whether a new initial condition is within the region of attraction of the nonlinear ODE on over 95% of a generated set of test data.",

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Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Region of Attraction Estimation (Reverse Time Van Der Pol Oscillator)

Cite this

Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Datasets

Region of Attraction Estimation (Reverse Time Van Der Pol Oscillator)

Cite this