State feedback control of des on the finite forbidden state problem

This paper addresses the state feedback control synthesis of discrete event systems on the forbidden state problem in which the forbidden states are finite, especially if they can not be expressed as linear inequality constraints using reported methods. The system is modelled by controlled Petri nets that ape bounded Petri nets or unbounded Petri nets with uncontrollable subnets satisfying the Reverse net Structurally Bounded Condition. Through the analysis of the reverse net, we obtain not only the weakly forbidden markings used to deal with uncontrollable transitions but also the maximally permissive state feedback control policy. Moreover, it is illustrated by an example in the reported literature that the method can be applied conveniently to a class of Petri nets whose uncontrollable subnets are Output Dominant Petri nets.