Verification of Uncertain Embedded Systems by Computing Reachable Sets Based on Zonotopes

Formal verification using reachability analysis has been shown to be useful for detecting design failures for controlled embedded systems, and thus to improve dependability. If the state space is hybrid, however, the growth of complexity with the dimension of the continuous dynamics limits the applicability significantly. This paper proposes an efficient approach to computing reachable sets for hybrid systems with time-varying linear continuous dynamics and uncertain inputs. The key idea is to combine zonotopes and polytopes for set representation when reachable sets are intersected with the transition guards which determine the discrete behavior of the hybrid system. Different methods for conservatively transforming zonotopes into polytopes (and vice versa) are proposed and experimentally compared.