Accurate reachability analysis of uncertain nonlinear systems

Abstract

We propose an algorithm to over-approximate the reachable set of nonlinear systems with bounded, time-varying parameters and uncertain initial conditions. The algorithm is based on the conservative representation of the nonlinear dynamics by a differential inclusion consisting of a linear term and the Minkowsky sum of two convex sets. The linear term and one of the two sets are obtained by a conservative first-order over-approximation of the nonlinear dynamics with respect to the system state. The second set accounts for the effect of the time-varying parameters. A distinctive feature of the novel algorithm is the possibility to over-approximate the reachable set to any desired accuracy by appropriately choosing the parameters in the computation. We provide an example that illustrates the effectiveness of our approach.