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

Reference:
B. De Schutter, T. van den Boom, J. Xu, and S.S. Farahani, "Analysis and control of max-plus linear discrete-event systems: An introduction," Discrete Event Dynamic Systems: Theory and Applications, vol. 30, pp. 25-54, 2020.

Abstract:
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.