ON THE OPTIMAL CONTROL OF DISCRETE EVENT SYSTEMS BASED ON SUPERVISORY CONTROL

摘要

Supervisory control belongs essentially to logic level for control problems in discrete event systems (DESs) and its corresponding control task is hard. This is unlike many practical optimal control problems which belong to the performance level and whose control tasks are soft. In this paper, we present a new model for optimal control in DESs based on the supervisory control. The performance measure is to minimize the maximal discounted total cost among all possible strings that the system generates. We present the optimality equation and obtain its optimal solution, which are stationary when the cost function is stationary. Then we use this new model to describe and solve uniformly the basic synthesizing problems in the event feedback control and the state feedback control in the supervisory control area. Moreover, we show that the languages and the predicates of control invariance with their permissive supervisors and state feedbacks not only have meanings in the supervisory control but are also the optimal solutions for some optimal control problems. This shows a link existing between the logic level and the performance level for the control of DESs. Finally, a numerical example is given to illustrate some results for the supervisory control in a DES.