Design of control laws for timed event graphs networks subject to mutual exclusion constraints in Min-Plus algebra

Abstract

The right control of systems, especially when different constraints exist, can avoid many problems of cost and time loss. This paper relates to the resolution of the mutual exclusion problem for discrete event systems modeled with a Network of Timed Event Graphs (NTEGs). It aims to propose formal approaches based on Min-Plus algebra formalisms for the synthesis of control laws to guarantee mutual exclusion constraints in NTEGs. In these studies, the behavior of the network is described by a set of linear Min-Plus equations and mutual exclusion specifications are represented by inequalities that are also linear in Min-Plus algebra. Computed laws are modeled by control places which are connected to the initial NTEGs in order to prevent the violation of mutual exclusion constraints.