Reachability Analysis of Nonlinear Discrete-Time Systems Using Polyhedral Relaxations and Constrained Zonotopes

Abstract

This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to propagate CZs through nonlinear functions, which is normally done using conservative linearization techniques. The new propagation method provides better approximations than those resulting from linearization procedures, leading to significant improvements in the computation of reachable sets in comparison to other CZ methods from the literature. Numerical examples highlight the advantages of the proposed algorithm.