Distributed implementations of Ramadge-Wonham supervisory control with Petri nets

Abstract

The purpose of the paper is to assess the benefits of using free labeled and bounded Petri nets as controllers, in the context of Ramadge and Wonham’s supervisory control theory. This theory allows, for several types of control problems expressed with regular languages, to decide when they are feasible and to produce finite control automata as solutions. The state graphs of free labeled and bounded Petri nets are a strict subclass of the finite automata. Concentrating on Petri net controllers can only lead to a weaker theory. The compact representation of net controllers is not a definite advantage since modular control synthesis may be used to a comparable effect in the framework of automata and their products. In order to reveal the major benefits of Petri net synthesis for supervisory control, we further impose on nets a structural constraint of distributability. Bounded and distributable nets translate to equivalent systems of finite message passing automata. Distributable net controllers induce therefore distributed control systems for distributed discrete event systems: each DES component receives as its local control component one of the message passing automata, and the locally controlled subsystems interact with one another in fully asynchronous mode. We study in this paper the implementation of Ramadge and Wonham’s finite state controllers by distributable net controllers.