Data-Driven Reachability of Nonlinear Lipschitz Systems via Koopman Operator Embeddings

Data-driven safety verification of robotic systems often relies on zonotopic reachability analysis due to its scalability and computational efficiency. However, for nonlinear systems, these methods can become overly conservative, especially over long prediction horizons and under measurement noise. We propose a data-driven reachability framework based on the Koopman operator and zonotopic set representations that lifts the nonlinear system into a finite-dimensional, linear, state-input-dependent model. Reachable sets are then computed in the lifted space and projected back to the original state space to obtain guaranteed over-approximations of the true dynamics. The proposed method reduces conservatism while preserving formal safety guarantees, and we prove that the resulting reachable sets over-approximate the true reachable sets. Numerical simulations and real-world experiments on an autonomous vehicle show that the proposed approach yields substantially tighter reachable set over-approximations than both model-based and linear data-driven methods, particularly over long horizons.