On the Synthesis of Optimal Schedulers in Discrete Event Control

This paper deals with a new type of optimal control for Discrete Event Systems. Our control problem extends the theory of 18], that is characterized by the presence of uncontrollable events, the notion of occurrence and control costs for events, and a worst-case objective function. A signiicant diierence with the work in 18] is that our aim is to make the system evolve through a set of multiple goals, one by one, with no order necessarily pre-speciied, whereas the previous theory only deals with a single goal. Our solution approach is divided into two steps. In the rst step, we use the optimal control theory in 18] to synthesize individual controllers for each goal. In the second step, we develop the solution of another optimal control problem, namely, how to modify if necessary and piece together, or schedule, all of the controllers built in the rst step in order to visit each of the goals with least total cost. We solve this problem by deening the notion of a scheduler and then by mapping the problem of nding an optimal scheduler to an instance of the well-known Traveling Salesman Problem (TSP) 7]. We nally suggest various strategies to reduce the complexity of the TSP resolution while still preserving global optimality.