Hybrid kernels and capture basins for impulse constrained systems

Abstract

We investigate, for constrained controlled systems with impulse, the subset of initial positions contained in a set K from which starts at least one run viable in K - the hybrid viability kernel - eventually until it reaches a given closed target in finite time - the hybrid capture basin. We define a constructive algorithm which approximates this set. The knowledge of this set is essential for control problem since it provides viable hybrid feed-backs and viable runs. We apply this method for approximating the Minimal Time-to-reach Function in the presence of both constraints and impulses. Two examples are presented, the first deals with a dynamical system revealing the complexity of the structure of hybrid kernels, the second deals with a Minimal Time problem with impulses.