On the optimal control of discrete event systems

The problem of the optimal control of systems accurately represented with a logical discrete-event system (DES) model is formulated and solved for the deterministic case. The given DES model P is thought of as characterizing the valid dynamical behavior of the physical plant. Another DES model A represents design objectives which specify the allowable DES behavior which is `contained in´ the valid behavior. Assuming that the allowable behavior can be attained, a controller can be constructed which will select a sequence of inputs that results in allowable plant behavior. The authors consider the case where there is another part of the design objectives which indicates that not only should the controller choose the plant inputs so that the plant behavior is allowable, but it should also, in some sense, be optimal. It is within this context that they formulate an optimal controller synthesis problem, i.e. how to construct a controller to achieve optimal allowable DES behavior. Their solution to this problem utilizes results from the theory of heuristic search to help overcome problems with computational complexity often encountered with logical DES models