Data-Driven Reachability Analysis for Nonlinear Systems

We consider the problem of forward reachability analysis of a closed-box nonlinear system, using only the data from the system. We propose a method that computes an ellipsoidal set that tightly over-approximates the true reachable set using convex optimization. Exploiting the fact that a linear approximation of a nonlinear system is not unique, we find conditions of a linear time-varying system that approximates the nonlinear system such that its reachable set is guaranteed to include the reachable set of the unknown nonlinear system, assuming that the Lipchitz coefficient of the nonlinear system is known. Then, we formulate a convex optimization problem that jointly searches for the parameters of the linear system and its ellipsoidal over-approximate reachable set based only on the data to minimize the growth rate of the reachable set while ensuring the ellipsoid over-approximates the true reachable set. We demonstrate the advantages of the proposed method via two illustrative examples: an autonomous nonlinear system and the TRAF22 benchmark system, and compare the results with other state-of-the-art algorithms.