Supervisor synthesis for enforcing linear constraints on a class of Petri nets with unobservable transitions
Ning Ran, Shouguang Wang, Hongye Su, Chengying Wang · IMA Journal of Mathematical Control and Information · 2015
It is important to solve the forbidden state problem in discrete event systems modelled by Petri nets with unobservable transitions. This paper studies the structurally optimal transformation for a class of Petri nets whose unobservable influence subnets are |$\alpha $| nets. First, the concepts of an unobservable influence subnet, an A-path, an A-circuit and an |$\alpha $| net are defined, and some of their properties are proposed. Next, a method is proposed to transform a given generalized mutual exclusion constraint into a structurally optimal one that can be enforced directly on the net in the form of monitor-based supervisors. It has high-computational efficiency since it is of polynomial complexity with respect to the net size. Finally, an example is used to illustrate the application of the proposed method.