Zonotopic Under-Approximations of Input Reachable Sets for Controllable Linear Systems

Abstract

Recent years have seen a surging interest in developing under-approximations of reachable sets due to their potential applications in control synthesis and verification. In this paper, we propose a method that yields under-approximations of finite-time input reachable sets for continuous-time controllable linear time-invariant systems with zonotopic input sets, utilizing approximations of the matrix exponential and its integral. The proposed method generates zonotopic under-approximations that converge in the sense of the Hausdorff distance. In addition, we introduce a variant of the proposed method that is better suited for applications with large time horizons. To illustrate its performance, we implement our proposed method in two numerical examples.