Tight Remainder-Form Decomposition Functions With Applications to Constrained Reachability and Guaranteed State Estimation

• 成果类型: Article
• 署名作者: Khajenejad, Mohammad; Yong, Sze Zheng
• 署名单位: University of California System; University of California San Diego; Northeastern University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3250515
• 发表日期: 2023
• 页码: 7057-7072
• 关键词: Nonlinear dynamical systems; reachability analysis; mixed-monotonicity; one-sided decomposition functions; ELLS systems

摘要

In this article, we propose a tractable family of remainder-form mixed-monotone decomposition functions that are useful for overapproximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous systems, which we show to be a strict superset of locally Lipschitz continuous systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the overapproximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise.