Data-Driven Reachability Analysis for Piecewise Affine Systems

Abstract: Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires determining whether system states can enter unsafe regions under given initial conditions and uncertainties, a question directly addressed by reachability analysis. However, hybrid systems present unique difficulties because their state space is divided into multiple regions with distinct dynamic models, causing traditional data-driven methods to produce inadequate over-approximations of reachable sets at region boundaries where dynamics change abruptly. This paper introduces a novel approach using hybrid zonotopes for data-driven reachability analysis of piecewise affine systems. Our method addresses the boundary transition problem by developing computational algorithms that calculate the family of set models guaranteed to contain the true system trajectories. Additionally, we extend and evaluate three methods for set-based estimation that account for input-output data with measurement noise.