Modelling and feedback control for a class of Petri Nets with shared resources subject to strict time constraints using Max-plus algebra

We address a modelling framework and a state feedback control problem of discrete event systems with shared resources using Max-plus algebra. In this paper, we consider the class of Networked Conflicting Timed Event Graphs (NCTEGs), which are timed Petri nets with conflicts, subjected to strict temporal constraints. Firstly, an algebraic formalisation in terms of switching Max-plus linear systems is proposed to describe the dynamic behaviour of a NCTEG. Secondly, closed-loop control laws are calculated to ensure the compliance of these time constraints imposed on a certain number of places. For this, sufficient conditions for the existence of such control laws have been provided. Finally, these theoretical approaches are illustrated by a realistic example of a time-critical railway network crossing system.