Algebraic Control Strategy for Solving the Mutual Exclusion Constraint Problem in a Network of Timed Event Graphs With Disturbance Inputs: Application to an Assembly Process

This paper addresses the control problem for a class of discrete event systems with disturbances, which is subject to mutual exclusion constraints (MECs). Our aim is to propose a new analytical method for designing control laws to guarantee a set of MECs in network timed event graphs (NTEGs) with uncontrollable input transitions. To develop this control law, linear min-plus equations are used to describe the behavior of the NTEGs and min-plus inequalities to translate the specifications to be satisfied. Sufficient conditions for the existence of causal control laws are established. These calculated laws are represented by control places that will supervise the NTEGs to ensure that constraints are respected. To demonstrate the effectiveness of the suggested approach, an illustrative application on an assembly system is carried out.