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

Brendon K. Colbert, Matthew Peet

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

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 languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2341-2347
Number of pages7
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

Lyapunov functions
Nonlinear systems
Nonlinear Systems
Trajectories
Trajectory
Nonlinear ODE
Estimate
Lyapunov Function
Initial conditions
Polynomials
Least Absolute Deviation
Predict
Testing
Sum of squares
Level Set
Converse
Vector Field
State Space
Polynomial

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Colbert, B. K., & Peet, M. (2019). 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., 2019. p. 2341-2347 8618959 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

Colbert, BK & Peet, M 2019, 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
Colbert BK, Peet M. Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2341-2347. 8618959. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8618959
Colbert, Brendon K. ; Peet, Matthew. / Using Trajectory Measurements to Estimate the Region of Attraction of Nonlinear Systems. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2341-2347 (Proceedings of the IEEE Conference on Decision and Control).
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