Supervisor Synthesis for Enforcing a Disjunction of GMECs on Controlled Petri Nets

A novel method is proposed to synthesize the optimal supervisors for a class of control problems in Petri nets. It is to enforce a disjunction of generalized mutual exclusion constraints (GMECs) on a plant net where influence uncontrollable subnets are forward synchronization and backward conflict free (FSBCF) nets. Note that it is a class of control problems that have not been solved. Using properties of FSBCF nets, the necessary and sufficient condition of the admissible marking is obtained. Then, based on this condition, the necessary and sufficient of the existence of the supervisor is presented, and the algorithm to design the optimal supervisor is given. An example is given to illustrate the theoretic results.