Supervisory Control of Systems Modeled by Petri Net from Adequate Admissible Constraints

The purpose of Supervisory Control of the system, considered as Discrete Event Systems (SED), is to synthesize an optimal and non-blocking controller. Indeed, the specifications of the SED are generally declined in forbidden states that must be avoided. Our work consisted in finding a structural synthesis approach based on the determination of the adequate admissible constraints stresses for the Petri net (PN) invariant method. The closed-loop system model (SED) is obtained by synchronous product of elementary PNs. First, we used the computational power of the Kumar algorithm based on finite state automata to determine the constraints related to forbidden states. But, exploration of the PN marking graph is laborious. This is what led us second, to represent the reachable marking graph by its transition matrix. The coding of this matrix, according to the state specification, allowed us to separate the states and identify the states relevant to the synthesis of a controller.