Data-Driven Reachability Analysis with Optimal Input Design
This work addresses safety verification for control systems where models are unknown, offering reduced conservatism through improved data collection and matrix inversion techniques.
This paper tackles the problem of conservatism in data-driven reachability analysis for unknown linear systems with noise by proposing two strategies: replacing the pseudoinverse with a row-norm-minimizing right inverse via SOCP, and introducing online A-optimal input design to improve data informativeness. Numerical results on stable LTI and piecewise affine systems show that combining these approaches significantly reduces conservatism compared to baseline methods, yielding tighter reachable sets for safety verification.
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.