On Petri Net Models of Infinite State Supervisors

We consider a class of supervisory control problems that require infinite state supervisors and introduce Petri nets with inhibitor arcs (PN's) to model the supervisors. We compare this PN-based approach to supervisory control to automata-based approaches. The primary advantage of a PN-based supervisory controller is that a PN-based controller provides a finite representation of an infinite state supervisor. For verification, implementation, and testing reasons, a finite PN-based representation of an infinite state supervisor is preferred over an automata-based supervisor. We show that this modeling advantage is accompanied by a decision disadvantage, in that in general the controllability of a language that can be generated by the closed-loop system is undecidable.