Controllable Firing Sequences in Event-Driven Systems
Toshimitsu Ushio, Ryuichi MATSUMOTO · Transactions of the Society of Instrument and Control Engineers · 1988
This paper deals with control problems in event-driven systems and controllable firing sequences. Event-driven systems are modelled by Petri nets with external input places. A control problem discussed in this paper is whether or not there exists a controller such that the set of firing sequences in a controlled system is equal to a desired one, which is called a desired firing set. This paper introduces a concept of a controllable firing set, which is a generalization of a controllable language defined by Ramadge and Wonham. Then, it is proved that the necessary and sufficient condition for the existence of such a controller is for the desired firing set to be a controllable one.This paper is also concerned with a generalization of the reachable problem discussed by Ichikawa, et al., which is called a target marking controllable problem in this paper, and gives the necessary and sufficient conditions for it.