On the existence of optimal solutions for the modular supervisory control of hybrid systems

This paper presents a modular approach to the supervisory control of hybrid systems that always leads to optimal solutions. The class of hybrid systems considered is such that threshold-crossing events in the continuous state space force discrete state transitions; and the continuous dynamics are determined by a discrete condition, which depends on the current discrete state of the system. The problem is to construct modular supervisors, each to satisfy a particular specification given in terms of sequences of threshold events, in such a way that the joint action of these supervisors results in an optimal (minimally restrictive) control action. The supervisors for the hybrid system are obtained using the theory of supervisor synthesis for discrete event systems. A procedure to guarantee the optimality of the solution is presented and an example is used to illustrate the proposed methodology.