Supervisor synthesis for bounded Petri nets based on a transformation function

This paper addresses the supervisor synthesis on the forbidden state problem, in which the forbidden markings cannot be easily expressed as linear inequality constraints using reported methods. The system to be controlled is modelled by bounded Petri nets with uncontrollable transitions. Through the analysis of the reverse net, we obtain the weakly forbidden markings in order to deal with uncontrollable transitions. By introducing a transformation function, which facilitates not only tracking the system state but also determining the control pattern, we propose a synthesis method to obtain the maximally permissive supervisor. The method need not analyze the reachability graph and the online computation has the complexity of polynomial times. In addition, for a special class of generalized Petri nets called the input dominant Petri nets, the synthesis method can be applied conveniently, as illustrated by an example in the reported literature.