Analysis and control of max-plus linear discrete-event systems: An introduction

• Published in: Discrete event dynamic systems Vol. 30; no. 1; pp. 25 - 54
• Main Authors: De Schutter, Bart, van den Boom, Ton, Xu, Jia, Farahani, Samira S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-03-2020; Springer Nature B.V
• Subjects: Algebra; Concurrency; Control; Control systems; Convex and Discrete Geometry; Discrete event systems; Electrical Engineering; Linear systems; Machines; Manufacturing; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Predictive control; Processes; Synchronism; Systems Theory; Model predictive control; Analysis of discrete-event systems; Survey; Residuation-based control; Max-plus algebra; Max-plus linear systems; Model-based control of max-plus linear systems
• ISSN: 0924-6703; 1573-7594
• DOI: 10.1007/s10626-019-00294-w

The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discrete-event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.