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

Abstract

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.

Keywords:

• Networked conflicting timed event graphs (NCTEGs)
• discrete event systems(DESs)
• switching Max-plus linear systems
• time constraints
• closed loop control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Sofiane Aberkane

Sofiane Aberkane received his master degree in automatic control from the Mouloud Mammeri University, Tizi-Ouzou, Algeria, in 2018. His is currently working towards a PhD degree about discrete event systems at the L2CSP laboratory in University of Mouloud Mammeri. His current research interests include control and modelling of discrete event systems using Petri nets and Max-Plus algebra.

Redouane Kara

Redouane Kara received the Ph.D. degree from the Mouloud Mammeri University, Tizi-Ouzou, Algeria, in 2009. He is currently a Professor at the University of Mouloud Mammeri. He carries out research at the Laboratoire de Conception et Conduite des Systemes de Production (L2CSP), Mouloud Mammeri University. His main research interests are analysis and control of discrete event systems.

Saïd Amari

Saïd Amari received the Ph.D. degree from the Institue of Research in Communications and Cybernetic oh Nantes, France, in 2005. He is currently an Associate Professor at the University of Paris 13. He carries out research at the automated Production Research Laboratory from the Ecole Normale Superieure Paris-Saclay. His main research interests are perfermance evaluation and control of discrete event systems using Petri nets and dioid algebra.