TY - GEN
T1 - Estimating the region of attraction using polynomial optimization
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
AU - Jones, Morgan
AU - Mohammadi, Hesameddin
AU - Peet, Matthew
N1 - Funding Information:
This research was carried out with the financial support of the NSF Grant CNS-1739990.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions whose sublevel sets approximate the true region of attraction arbitrarily well. The main technical result of the paper is the proof of existence of such a Lyapunov function. Specifically, we use the Hausdorff distance metric to analyze convergence and in the main theorem demonstrate that the existence of an n-times continuously differentiable maximal Lyapunov function implies that for any ϵ > 0, there exists a polynomial Lyapunov function and associated sub-level set which together prove stability of a set which is within e Hausdorff distance of the true region of attraction. The proposed iterative method and probably convergence is illustrated with a numerical example.
AB - In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions whose sublevel sets approximate the true region of attraction arbitrarily well. The main technical result of the paper is the proof of existence of such a Lyapunov function. Specifically, we use the Hausdorff distance metric to analyze convergence and in the main theorem demonstrate that the existence of an n-times continuously differentiable maximal Lyapunov function implies that for any ϵ > 0, there exists a polynomial Lyapunov function and associated sub-level set which together prove stability of a set which is within e Hausdorff distance of the true region of attraction. The proposed iterative method and probably convergence is illustrated with a numerical example.
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U2 - 10.1109/CDC.2017.8263908
DO - 10.1109/CDC.2017.8263908
M3 - Conference contribution
AN - SCOPUS:85046138772
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 1796
EP - 1802
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 12 December 2017 through 15 December 2017
ER -