Backward Reachability for Polynomial Systems on a Finite Horizon

• 成果类型: Article
• 署名作者: Yin, He; Arcak, Murat; Packard, Andrew; Seiler, Peter
• 署名单位: University of California System; University of California Berkeley; University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3056611
• 发表日期: 2021
• 页码: 6025-6032
• 关键词: Constrained control; Nonlinear systems; reachable sets estimation; uncertain systems

摘要

A method is presented to obtain an inner-approximation of the backward reachable set of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are formulated as nonlinear optimization problems, which are decoupled into tractable subproblems and solved by an iterative algorithm using the polynomial S-procedure and sum-of-squares techniques. This framework is also extended to uncertain nonlinear systems with L-2 disturbances and L-infinity parametric uncertainties. The effectiveness of the method is demonstrated on several nonlinear robotics and aircraft systems with control saturation.