Monotone Numerical Schemes and Feedback Construction for Hybrid Control Systems

Abstract

Hybrid systems are a general framework which can model a large class of control systems arising whenever a set of continuous and discrete dynamics are mixed in a single system. In this paper, we study the convergence of monotone numerical approximations of value functions associated to control problems governed by hybrid systems. We discuss also the feedback reconstruction and derive a convergence result for the approximate feedback control law. Some numerical examples are given to show the robustness of the monotone approximation schemes.