Optimal Nonblocking Directed Control of Discrete Event Systems

For the control of discrete event systems, the notion of directed control refines that of supervisory control. A directed controller is one that selects at most one controllable event to be enabled at any state (without disabling any uncontrollable event), which is in fact how a discrete event control is implemented. In contrast, a supervisory controller computes a maximal allowable set of controllable events at each state, leaving undecided exactly which controllable event should be enabled. In previous works, we developed a framework for the computation of optimal directed controllers and a polynomial synthesis algorithm for acyclic plants. In this paper, we present a novel synthesis approach for general plants, i.e., plants with or without cycles, thus providing a complete solution to the optimal directed control problem. The complexity of the approach remains polynomial in the size of plant.