A synthesis of state avoidance policies for a class of controlled Petri nets with weighted arcs

In this paper, a new method is proposed for synthesizing state avoidance policies for a class of controlled Petri nets with weighted arcs (WCPNs) which can model process synchronization, resource conflicts and buffer overflows. The forbidden states of WCPNs are represented by both a forbidden place set and the number of total tokens in the places of the forbidden place set in order to handle forbidden states of nonbinary markings. This paper derives necessary and sufficient conditions for admissible markings and boundary markings in terms of a precedence subnet and a boundary subnet. Also, a maximally permissive control is presented in WCPNs, which is applied to a partially controllable multiproduct batch process plant.