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This paper proposes methods for reachability analysis of nonlinear systems inboth open loop and closed loop with advanced controllers. The methods combinehybrid zonotopes, a construct called a state-update set, functionaldecomposition, and special ordered set approximations to enable linear growthin both reachable set memory complexity and computational complexity with time.Facilitating this combination are new identities for constructing nonconvexsets that contain nonlinear functions and for efficiently converting acollection of polytopes from vertex representation to hybrid zonotoperepresentation. Numerical examples demonstrate reachability analysis of acontinuous-time nonlinear system in closed loop with a neural networkcontroller trained using nonlinear model predictive control and ahigh-dimensional logical system.

Reachability Analysis of Nonlinear Systems Using Hybrid Zonotopes and Functional Decomposition