Combined Supervisor Synthesis Based on Constraint Transformation

Based on constraint transformation, a novel method to synthesize combined supervisors is proposed to solve a class of control problems in Petri nets. The control specification is a conjunction of generalized mutual exclusion constraints (GMECs) where influence uncontrollable subnets are forward synchronization and backward conflict free (FSBCF) nets. An element generalized mutual exclusion constraint (EGMEC) is introduced, and it is a GMEC such that there is only one forbidden place, and its input transitions are all controllable. Then a method is presented to design the observer places. Furthermore, a method is given to transform a conjunction of GMECs into a conjunction of EGMECs using observer places. An algorithm is proposed to enforce a conjunction of EGMECs or a disjunction of GMECs on a Petri net. Lastly, an example is given to illustrate the theoretic results.