This paper addresses the forbidden state problem of Petri nets (PN) with liveness requirement and uncontrollable transitions. The proposed approach computes a maximally permissive PN controller, whenever such a controller exists. The first step, based on a Ramadge-Wonham-like reasoning (1989), determines the legal and live maximal behavior the controlled PN should have. In the second step, the theory of regions is used to design control places to add to the original model to realize the desired behavior. Furthermore, necessary and sufficient conditions for the existence of control places realizing the maximum permissive control are given. A parameterized manufacturing application of significant state space is used to show the efficiency of the proposed approach.

Forbidden state problem of Petri nets with non-blocking requirement and uncontrollable transitions is addressed in this paper. The approach proposed in this paper combines the Ramadge-Wonham's (1989) approach and the theory of regions, a theory recently proposed for compiling a labelled automaton into a Petri net. It first determines the automaton model of the closed loop system using a Ramadge-Wonham-like approach. It then uses the theory of regions to design a set of control places to add to the initial Petri net to realize the maximum permissive and non-blocking control. Although the proposed approach does not avoid the state explosion problem in its design phase, it does provide a compact representation of the optimum control in terms of control places and hence can be very useful in the implementation of optimum control.