Nonblocking Directed Control of Discrete Event Systems

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 specific selection for executing an enabled event is made. While a supervisor design 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 prove that a nonblocking director exists if and only if a nonblocking supervisor exists, thereby proving the polynomiality of verifying existence. We also develop a set of algorithms of polynomial complexity to compute a nonblocking director.