Reachability Analysis of Nonlinear Systems Using Hybridization and Dynamics Scaling

Abstract

Reachability analysis techniques aim to compute which states a dynamical system can enter. The analysis of systems described by nonlinear differential equations is known to be particularly challenging. Hybridization methods tackle this problem by abstracting nonlinear dynamics with piecewise linear dynamics around the reachable states, with additional inputs to ensure overapproximation. This reduces the analysis of a system with nonlinear dynamics to the one with piecewise affine dynamics, which have powerful analysis methods. In this paper, we present improvements to the hybridization approach based on a dynamics scaling model transformation. The transformation aims to reduce the sizes of the linearization domains, and therefore reduces overapproximation error. We showcase the efficiency of our approach on a number of nonlinear benchmark instances, and compare our approach with Flow*.