Reachability Analysis Using Hybrid Zonotopes and Functional Decomposition

This paper proposes methods for reachability analysis of nonlinear systems, including those in closed loop with nonlinear controllers such as neural networks. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time steps and linear scaling in time complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.