Petri nets as discrete event models for supervisory control

Abstract

Discrete event systems represents a new field of control theory of increasing importance in the domains of manufacturing, communications, and robotics. Supervisory Control theory, based on formal languages, is a well established framework for the study of discrete event systems. The thesis discusses the use of Petri nets in Supervisory Control. Place/Transition nets have been used by several authors to represent discrete event systems. In our approach, the supervisor, i.e., the control agent that restricts the behavior of a system within a legal behavior, is represented as a Place/Transition net as well. The advantage of such a supervisor, as opposed to a supervisor given as a feedback function, is that a closed loop model of the controlled system may be constructed and analyzed using the techniques pertaining to Petri net models. We show that a Petri net supervisor may not exist if the system's behavior or the legal behavior are nonregular Petri net languages. By defining a new class of Petri net languages, called deterministic P-closed, it is possible to derive necessary and sufficient conditions for the existence of supervisors as nets. The thesis presents an algorithm, based on the concurrent composition operator, for the design of Petri net supervisors and discusses how a composed net may be validated. In a first approach, based on incidence matrix analysis, important properties of the net, such as controllability or such as the absence of blocking states, may be studied by Integer Programming techniques. In a second approach, we consider a class of specifications, called generalized mutual exclusion constraints, and discuss several possible structures for the supervisor capable of enforcing them.