ABSTRACT

This chapter presents two general approaches for Petri net (PN) supervisory control. The first is the GMEC-based approach, which allows nice PN controller design under some GMEC specifications. The second is a state-space-based approach and is based on a so-called theory of regions, which allows design of optimal PN controllers under fairly general conditions. The theory of region approach can be easily adapted to determine a control place for any event separation instance by limiting the reachability constraint to stable markings and firability constraints to those of original transitions. The control algorithm can be adapted appropriately by not checking the firability of FIFO transitions, that is unstable markings can be negative. The essentially safe petri net (ESPN) transformation of a bounded PN first identifies a set of places called state places such that any remaining place forms a P-invariant with state places.