Overapproximating Reachable Tubes of Linear Time-Varying Systems

• 成果类型: Article
• 署名作者: Serry, Mohamed; Reissig, Gunther
• 署名单位: University of Waterloo; Bundeswehr University Munich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3057504
• 发表日期: 2022
• 页码: 443-450
• 关键词: Electron tubes; uncertainty; Time-varying systems; Ellipsoids; nonlinear dynamical systems; viscosity; STANDARDS; linear time-varying (LTV) systems; reachability

摘要

We present a method to overapproximate reachable tubes over compact time intervals for linear continuous-time time-varying control systems, whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic overapproximations. The performance of the latter variant is demonstrated on an example.