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Control and State Estimation for max-plus Linear Systems

机译：最大线性系统的控制和状态估计

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Max-plus linear systems theory was inspired by and originated from classical linear systems theory more than three decades ago, with the purpose of dealing with nonlinear synchronization and delay phenomena in timed discrete event systems in a linear manner. Timed discrete event systems are driven by discrete events, are equipped with a notion of time, and their temporal evolution is entirely characterized by the occurrence of events over time. If their behavior is completely governed by synchronization and delay phenomena, timed discrete event systems can be modeled as max-plus linear systems. On appropriate levels of abstraction, such systems adequately describe many problems in diverse areas such as manufacturing, communication, or transportation networks. The aim of this paper is to provide a thorough survey of current research work in max-plus linear systems. It summarizes the main mathematical concepts required for a theory of max-plus linear systems, including idempotent semirings, residuation theory, fixed point equations in the max-plus algebra, formal power series, and timed-event graphs. The paper reviews some recent major achievements in control and state estimation of max-plus linear systems. These include max-plus observer design, max-plus model matching by output or state feedback and observer-based control synthesis. Control is required to be optimal with respect to the so-called just-in-time criterion, which is a common standard in industrial engineering. It implies that the time for all input events is delayed as much as possible while guaranteeing that all output events occur, at the latest, at pre-specified reference times.
机译：Max-Plus线性系统理论的灵感来自三十多年前的经典线性系统理论，目的是以线性方式处理非线性同步和延迟现象。定时离散事件系统由离散事件驱动，配备了时间的概念，其时间演变完全以事件的发生随着时间的推移发生。如果它们的行为完全由同步和延迟现象完全控制，则可以将定时离散事件系统建模为最大线性系统。在适当水平的抽象水平上，此类系统充分描述了制造，通信或运输网络等不同领域的许多问题。本文的目的是对最高线性系统中当前的研究工作进行全面调查。它总结了最大值线性系统理论所需的主要数学概念，包括同性恋半径，残留理论，最大值代数中的固定点方程，正式幂序列和定时事件图。本文回顾了最新的最高线性系统估计和状态估计的一些主要成就。其中包括最大值观察者设计，通过输出或状态反馈和基于观察者的控制合成的最大值模型匹配。对于所谓的即时标准，控制必须是最佳的，这是工业工程中的常见标准。这意味着所有输入事件的时间都会尽可能延迟，同时确保所有输出事件最新发生在预先指定的参考时间上。

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