Optimal Control of a Class of Discrete Event Systems

Abstract

We formulate and solve a new optimal control problem for a class of discrete event systems. We assume that the system can be modeled as a finite acyclic directed graph, i.e.. it has a finite set of event trajectories. The optimal control problem explictly considers the cost of control in the objective function. In general terms, this problem involves a tradeoff between the cost of system evolution, which is quantified in terms of a path cost on the event trajectories generated by the system, and the cost of impacting on the external environment, which is quantified as a dynamic cost on control. An algorithm based on dynamic programming is developed for the solution of this problem. T his algorithm is based on a graph-theoretic formulation of the problem. The use of dynamic programming allows for the efficient construction of an “optimal subgraph” (i.e., optimal supervisor) of the given graph (i.e., discrete event system) with respect to the cost structure imposed.