Control Synthesis

The controller ``agent'' of R&W consists of a pair where S is a recognizer for a ``proper'' supervisor, and is a ``control pattern'' defined by , such that the event is enabled by if , and disabled by if . This function can be extended over by defining for all , so that the control pattern would always leave ``enabled'' an event that cannot be controlled.
The generator does not represent, in general, a ``proper'' supervisor, as it may possess any of the following ``bad'' states:

• Blocking states from which marker states cannot be reached. See for the Two-Pusher Example (Section 6.1) for an illustration of blocking states.
• Non-controllable states from which an uncontrollable event is enabled in P but not in . We have no such states in the legal language for the Two-Pusher Example.

Blocking states and non-controllable states must be removed from in order to obtain S. This means we must disable the controllable events that lead to blocking states, or to states from which a forbidden uncontrollable event is possible. The control map is then obtained from the proper recognizer S. Figure 10 shows the proper supervisor for the Two-Pusher Example, and Table 1 gives the control map .