期刊
ISA TRANSACTIONS
卷 136, 期 -, 页码 308-322出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.isatra.2022.11.015
关键词
Non-symmetric and unbounded region of attraction; Shape function; Polynomial nonlinear system; Sum of squares programming; Lyapunov stability
In this study, a cost-effective approach for ROA estimation is proposed based on Lyapunov theory and shape functions. The proposed method significantly improves the accuracy of ROA estimation compared to existing methods.
Sum-of-squares programming is widely used for region of attraction (ROA) estimations of asymptotically stable equilibrium points of nonlinear polynomial systems. However, existing methods yield conservative results, especially for non-symmetric and unbounded regions. In this study, a costeffective approach for ROA estimation is proposed based on the Lyapunov theory and shape functions. In contrast to existing methods, the proposed method iteratively places the center of a shifted shape function (SSF) close to the boundary of the acquired invariant subset. The set of obtained SSFs yields robust ROA subsets, and R-composition is employed to express these independent sets as a single but richer-shaped level set. Several benchmark examples show that the proposed method significantly improves ROA estimations, especially for non-symmetric or unbounded ROA without a significant computational burden.(c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.
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