Optimal Control Synthesis for a Flexible Manufacturing System Based on Minimal Cuts

This paper deals with supervisory control synthesis of Petri net controller for forbidden state transition problem based on a new utilization of the theory of regions. Two different approaches are proposed to reduce the resolution complexity of the theory of regions by minimizing the total number of equations in its linear system. These two approaches are based on a new concept of minimal cuts in reachability graph. The supervisor is a Petri net controller for each minimal cut. Moving from one control place to another allows the switch of minimal cuts in the reachability graph. These new approaches allows also to determine a Petri net controller when it doesn't exist using the classical approach of the theory of regions. To illustrate the present methods an application is implemented on the Flexible Manufacturing System (FMS) at the ENIM (National school of engineering of Metz) in FRANCE.