Max-plus algebra and max-plus linear discrete event systems: An introduction

We provide an introduction to 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. We also briefly present some control approaches for max-plus linear discrete event systems, including model predictive control. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.