Supervisory control of DES using the positive invariance property

This document presents a method for the supervisory control of the discrete event systems modeled by Petri nets based on positive invariance property, largely used in the field of control and analysis of continuous systems. Contrary to the structural approach, this method gives necessary and sufficient conditions of inhibition/authorization of firing transitions ensuring the invariance of the polyhedron of constraints, with the assumption that the transitions of the given net are all controllable. This method gives for each transition, in which side (of space) it must be authorized in order to satisfy polyhedron constraints and the enabling condition of the considered transition.