Data-Driven Reachability Analysis with Optimal Input Design

TL;DR

This paper introduces a data-driven approach to reduce conservatism in reachability analysis of unknown linear systems by optimizing input design and matrix inversion methods, resulting in tighter safety guarantees.

Contribution

It proposes a novel combination of input design and matrix inversion techniques within the CMZ framework to improve the accuracy of reachability over-approximations.

Findings

Tighter reachable sets achieved with designed inputs and row-norm right inverse.

Significant reduction in conservatism compared to baseline methods.

Validated on 5D LTI and 2D piecewise affine systems.

Abstract

This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available. Building on the constrained matrix zonotope (CMZ) framework, two complementary strategies are proposed to reduce conservatism in reachable-set over-approximations. First, the standard Moore--Penrose pseudoinverse is replaced with a row-norm-minimizing right inverse computed via a second-order cone program (SOCP), which directly reduces the size of the resulting model set, yielding tighter generators and less conservative reachable sets. Second, an online A-optimal input design strategy is introduced to improve the informativeness of the collected data and the conditioning of the resulting model set, thereby reducing uncertainty. The proposed framework extends naturally to piecewise affine systems through mode-dependent data partitioning. Numerical results on a five-dimensional stable LTI system and a two-dimensional piecewise affine system demonstrate that combining designed inputs with the row-norm right inverse significantly reduces conservatism compared to a baseline using random inputs and the pseudoinverse, leading to tighter reachable sets for safety verification.