Underapproximate Reachability Analysis for a Class of Linear Systems With Inputs

• 成果类型: Article
• 署名作者: Serry, Mohamed; Liu, Jun
• 署名单位: University of Waterloo; University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3276290
• 发表日期: 2024
• 页码: 1125-1132
• 关键词: Hausdorff distance; linear uncertain systems; matrix lower bounds; underapproximations

摘要

Underapproximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available underapproximation methods applicable to continuous-time linear systems typically assume the ability to compute transition matrices and their integrals exactly, which is not feasible in general, and/or suffer from high computational costs. In this note, we attempt to overcome these drawbacks for a class of linear time-invariant (LTI) systems, where we propose a novel method to underapproximate finite-time forward reachable sets and tubes, utilizing approximations of the matrix exponential and its integral. In particular, we consider the class of continuous-time LTI systems with an identity input matrix and initial and input values belonging to full-dimensional sets that are affine transformations of closed unit balls. The proposed method yields computationally efficient underapproximations of reachable sets and tubes, when implemented using zonotopes, with first-order convergence guarantees in the sense of the Hausdorff distance. To illustrate its performance, we implement our approach in three numerical examples, where linear systems of dimensions ranging between 2 and 200 are considered.