Ellipsoidal Techniques for Hybrid Dynamics: the Reachability Problem

Abstract

This paper deals with the dynamics of hybrid systems under piecewise open-loop controls restricted by hard bounds. The system equations may be reset when crossing some prespecified domains (“the guards”) in the state space. Therefore the continuous dynamics which govern the motion between the guards are complemented by discrete transitions which govern the resets. A state space model for such systems is proposed and reachability sets for such models are described. The computational side of reachability is treated through ellipsoidal techniques that indicate routes for numerical algorithms.