This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in both reachable set memory complexity and computational complexity with time. 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. Numerical examples demonstrate reachability analysis of a continuous-time nonlinear system in closed loop with a neural network controller trained using nonlinear model predictive control and a high-dimensional logical system.
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