Decidable Hybrid Systems

Hybrid systems combine differential equations with discrete event systems. We consider the reachability problem: is there a trajectory from an initial state to a target state in the hybrid system. We show that for hybrid systems with decoupled differential inclusions, the reachability problem can be decided in a finite number of steps. 1 Introduction Complex systems that are being designed today, incorporate both differential equations to model the continuous behavior, and discrete event systems to model instantaneous state changes in response to events. System which incorporate both dynamical and discrete event models are called hybrid systems. In this paper we study properties of hybrid automata --- a formalism for specifying hybrid systems. In particular, we are interested in algorithmic methods for solving problems relating to hybrid systems. Hybrid systems in which a problem can be solved algorithmically in a finite number of steps are called decidable hybrid systems. We consider..