On Petri net models of infinite state supervisors

A class of supervisory control problems that require infinite state supervisors is considered, and Petri nets with inhibitor arcs (PNs) are introduced to model the supervisors. This PN-based approach to supervisory control is compared to automata-based approaches. The primary advantage of a PN-based supervisory controller is that it 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. It is shown 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