Feedback Control Logic for Backward Conflict Free Choice Nets

The forbidden state problem in the context ofsupervisory control of discrete event systems modelled by Petrinets is discussed. The forbidden state problem is specified by generalized mutualexclusion constraints (GMECs). The case of backward conflict freeand free choice uncontrollable subnet is considered. Theuncontrollable subnet is first extended to a number of well formedfree choice nets and then decomposed in marked graph components, thatcan be obtained from minimal T-invariants of theextended net. The forbidden state problem is so re-formulated intoan equivalent one, based on the decomposed net, such that it can besolved by a linear programming problem. Thus, a polynomialcomplexity solution, suitable for on-line control, is achieved,improving the existing results in literature for this net subclass.