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.

中文翻译：

---

最大加线性离散事件系统的分析与控制：介绍

本文的目的是简要介绍最大加代数和最大加线性离散事件系统。我们介绍了最大加代数的基本概念，并解释了如何使用它来模拟特定类别的具有同步但没有并发的离散事件系统。这种系统被称为最大加线性离散事件系统，因为它们可以用最大加代数中的“线性”模型来描述。我们讨论了 max-plus 代数的一些关键性质，并说明了如何使用这些性质来分析 max-plus 线性离散事件系统的行为。接下来，简要介绍了最大加线性离散事件系统的一些控制方法，包括基于残差的控制和模型预测控制。最后，