Li, DongyangIgnatyev, DmitryTsourdos, AntoniosWang, Zhongyuan2022-11-242022-11-242022-09-21Li D, Ignatyev D, Tsourdos A, Wang Z. (2023) Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition. ISA Transactions, Volume 136, May 2023, pp. 308-3220019-0578https://doi.org/10.1016/j.isatra.2022.11.015https://dspace.lib.cranfield.ac.uk/handle/1826/18741Sum-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 cost-effective 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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Non-symmetric and unbounded region of attractionShape functionPolynomial nonlinear systemSum of squares programmingLyapunov stabilityArticle