Theory of Regions for Control Synthesis without Computing Reachability Graph

Sadok Rezig,Nidhal Rezg,Zied Achour

doi:10.3390/app7030270

Sadok Rezig, Nidhal Rezg + Show 1 more

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https://doi.org/10.3390/app7030270

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Abstract

This paper addresses the design of Petri net (PN) supervisor using the theory of regions for forbidden state problem with a set of general mutual exclusion constraints. In fact, as any method of supervisory control based on reachability graph, the theory of regions suffers from a technical obstacle in control synthesis, which is the necessity of computing the graph at each iteration step. Moreover, based on the reachability graph, which may contain a large number of states, with respect to the structural size of the system, the computation of PN controllers becomes harder and even impossible. The main contribution of this paper, compared to previous works, is the development of a control synthesis method in order to decrease significantly the computation cost of the PN supervisor. Thus, based on PN properties and mathematical concepts, the proposed methodology provides an optimal PN supervisor for bounded Petri nets following the interpretation of the theory of regions. Finally, case studies are solved by CPLEX software to compare our new control policy with previous works which use the theory of regions for control synthesis.

Highlights

Petri nets (PNs) present an effective tool to model and analyze Discrete Event Systems [1].They have compact structures and can be represented in the form of matrices
The proposed control synthesis method can be implemented for Flexible manufacturing system (FMS) and generally for bounded
The underlying notion of the previous work is that the theory of regions (TR) must be solved by handling a number of markings which may increase according to the structural size of the system

Summary

Introduction

Petri nets (PNs) present an effective tool to model and analyze Discrete Event Systems [1]. They have compact structures and can be represented in the form of matrices. PNs can be analyzed by linear algebras They play an important role in addressing the deadlock problems and analyzing the behavior of flexible manufacturing system [2,3,4,5]; a flexible manufacturing system can be defined as a computer controlled production system capable of processing a variety of part types. A Petri net is a directed graph consisting of places, transitions and valued arcs connecting them. Let p(t) (respectively, (t) p) be the set of output transitions (respectively, input transitions) of the place p.

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