Supervisor synthesis for a class of forbidden state problems in Petri nets

This paper describes a method for synthesizing an optimal supervisor for a controlled Petri net. The considered class of control problems is to enforce a conjunction of general mutual exclusion constraints (GMEC) on a controlled Petri net, in which the influence uncontrollable subnets are forward synchronization and backward conflict free (FSBCF) nets. An FSBCF net is an ordinary Petri net in which each transition has exactly one input place, and each place has exactly one output transition. Its properties are given. Based on these properties, the criterion of the admissible markings is obtained in the form of a conjunction of linear inequalities. Then it is utilized to obtain the necessary and sufficient condition of the existence of the supervisor, and to construct the method to synthesize the optimal supervisor. Note that the supervisor can be online computed within polynomial times. The theoretical results are illustrated by the synthesis of the output-port controllers (OPC) of an asynchronous transfer mode (ATM) switch