Maximally permissive and non-blocking control of Petri nets using theory of regions

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.