Reachability Analysis of Generalized Input-Affine Systems with Bounded Measurable Time-varying Uncertainties

Francois Bidet (1) , Eric Goubault (1) , Sylvie Putot (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

This paper presents an approach to overapproximate the reachable set of states of a system whose uncertainties are arbitrarily time-varying. Most approaches generally assume piecewise continuity or sometimes Riemannintegrability of the uncertainties. In this paper 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 overapproximation 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.

Mots clés: Switched systems; Time-varying systems; Uncertain systems

Domaines: Informatique [cs]

Francois Bidet, Eric Goubault, Sylvie Putot. Reachability Analysis of Generalized Input-Affine Systems with Bounded Measurable Time-varying Uncertainties. IEEE Control Systems Letters, 2022, 6, pp.638-643. ⟨10.1109/LCSYS.2021.3084530⟩. ⟨hal-03805968⟩