Reachability Analysis of Hybrid Systems Using Support Functions

Colas Le Guernic (1) , Antoine Girard (2)

1 VERIMAG - IMAG - VERIMAG
2 CASYS - Calculs Algébriques et Systèmes Dynamiques

This paper deals with conservative reachability analysis of a class of hybrid systems with continuous dynamics described by linear differential inclusions, convex invariants and guards, and linear reset maps. We present an approach for computing over-approximations of the set of reachable states. It is based on the notion of support function and thus it allows us to consider invariants, guards and constraints on continuous inputs and initial states defined by arbitrary compact convex sets. We show how the properties of support functions make it possible to derive an effective algorithm for approximate reachability analysis of hybrid systems. We use our approach on some examples including the navigation benchmark for hybrid systems verification.

Domaines: Optimisation et contrôle [math.OC]

Colas Le Guernic, Antoine Girard. Reachability Analysis of Hybrid Systems Using Support Functions. CAV 2009 - 21st International Conference on Computer Aided Verification, Jun 2009, Grenoble, France. pp.540-554, ⟨10.1007/978-3-642-02658-4_40⟩. ⟨hal-00769527⟩