Directed control of discrete event systems: optimization based approach

We introduce the notion of directed control, where a directed controller, simply referred as director, is one that selects at most one controllable event to be enabled at any instant. This is in contrast to supervisory control, where a supervisory controller, simply referred as supervisor, enables a maximum allowable set of controllable events at any instant, i.e., no selection for executing an enabled event is made. While design of a supervisor is meaningful for plants that are generator of controllable events, a director design makes more sense for plants that are executor of controllable events. In this paper we develop an optimization based approach for the design of a director: Starting from any state, the worst cost to the nearest reachable marked state is minimized. The motivation is that a pending task be completed in the least possible cost. A necessary and sufficient condition for the existence of an optimal director is obtained. Furthermore, for systems that are cycle-free, we provide an algorithm of polynomial complexity to compute an optimal director