Hierarchical Control Synthesis for Eventuality Specifications in Hybrid Systems

Abstract

In this paper a systematic methodology to derive controllers for hybrid automata which satisfy eventuality specifications is presented. Since the considered class of automata accepts both continuous and discrete control inputs a two level hierarchical control architecture is proposed. Due to the existence of disturbance inputs, the problem is studied in a game theoretic framework. We show that a least restrictive eventuality controller does not exist and we propose a dynamic programming algorithm that determines the maximal set of initial states from which there exists a solution to the problem and specifies the controller. The controller is finally extracted as the solntion to a system of Hamilton-Jacobi equations