A Polynomial-Based Approach of Reachable Set Estimation for Periodic Time-Varying Systems

• 成果类型: Article
• 署名作者: Ling, Zhaoji; Xie, Xiaochen; Lam, James; Kwok, Ka-Wai
• 署名单位: Harbin Institute of Technology; University of Hong Kong; Chinese University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3554703
• 发表日期: 2025
• 页码: 6167-6174
• 关键词: estimation; Time-varying systems; POLYNOMIALS; Symmetric matrices; Lyapunov methods; Harmonic analysis; Vehicle dynamics; vectors; Power harmonic filters; Gears; Matrix polynomial; multiaffine polynomial; periodic time-varying systems; reachable set estimation

摘要

This article is focused on estimating reachable sets for periodic time-varying systems, whose dynamics are represented by trigonometric series through Fourier theory. Given the difficulty of dealing with coupled time-varying coefficients in reachable set estimation, a constructive polynomial-based approach is utilized to transform time-varying nonconvex constraints into constant vertex constraints through the property of multiaffine matrix polynomials. Based on that, when the decay rate parameters for Lyapunov functions are known, the reachable set bounding region can be determined by solving vertex constraints in linear matrix inequality forms. In cases where the decay rates are unknown, a simulated annealing algorithm and a Boundary Intersection algorithm are proposed to provide a tractable solution for parameter searching, and to achieve lower conservatism in the reachable set bounding regions. The effectiveness of our polynomial-based approach is illustrated through simulations using a single-mesh gear system. Moreover, the efficiency of the two algorithms can be assessed by contrasting the conservatism reduced in measurements of bounding regions.