Inner-approximate Reachability Computation via Zonotopic Boundary Analysis

TL;DR

This paper introduces a novel boundary-based method using zonotopes for inner-approximate reachability analysis of dynamical systems, improving efficiency and accuracy over existing techniques.

Contribution

It proposes boundary and tiling matrix techniques for efficient boundary extraction and a flexible outer-approximation contraction to refine inner-approximations.

Findings

The method is more efficient than state-of-the-art approaches.

It produces less conservative inner-approximations.

Numerical results confirm high accuracy and effectiveness.

Abstract

Inner-approximate reachability analysis involves calculating subsets of reachable sets, known as inner-approximations. This analysis is crucial in the fields of dynamic systems analysis and control theory as it provides a reliable estimation of the set of states that a system can reach from given initial states at a specific time instant. In this paper, we study the inner-approximate reachability analysis problem based on the set-boundary reachability method for systems modelled by ordinary differential equations, in which the computed inner-approximations are represented with zonotopes. The set-boundary reachability method computes an inner-approximation by excluding states reached from the initial set's boundary. The effectiveness of this method is highly dependent on the efficient extraction of the exact boundary of the initial set. To address this, we propose methods leveraging boundary and tiling matrices that can efficiently extract and refine the exact boundary of the initial set represented by zonotopes. Additionally, we enhance the exclusion strategy by contracting the outer-approximations in a flexible way, which allows for the computation of less conservative inner-approximations. To evaluate the proposed method, we compare it with state-of-the-art methods against a series of benchmarks. The numerical results demonstrate that our method is not only efficient but also accurate in computing inner-approximations.