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.

Original languageEnglish
Pages (from-to)25-54
JournalDiscrete Event Dynamic Systems: theory and applications
Issue number1
Publication statusPublished - 2020

    Research areas

  • Analysis of discrete-event systems, Max-plus algebra, Max-plus linear systems, Model predictive control, Model-based control of max-plus linear systems, Residuation-based control, Survey

ID: 67600748