Reachability Analysis of Generalized Input-Affine Systems With Bounded Measurable Time-Varying Uncertainties

Abstract

This letter presents an approach to over-approximate the reachable set of states of a system whose uncertainties are arbitrarily time-varying. Most approaches generally assume piecewise continuity or sometimes Riemann-integrability of the uncertainties. In this letter we go one step further, only assuming Lebesgue measurability, which is the weakest meaningful hypothesis. We develop our new technique, based on a decomposition of components as a difference of positive functions, for separable systems, a generalization of control-affine systems. We compare the over-approximation produced by our method with the ones obtained using the tools Flow* and CORA on simple examples, and show that correct outer-approximations of the reachable sets are computable with a high degree of precision even for these general forms of uncertainties.