Timed Event Graphs (TEGs) can be described by time invariant (max,+) linear systems. This formalism has been studied for modelling, analysis and control synthesis for decision-free timed Discrete Event Systems (DESs), for instance specific manufacturing processes or transportation networks operating under a given logical schedule. However, many applications exhibit time-variant behaviour, which cannot be modelled in a standard TEG framework. In this paper we extend the class of TEGs in order to include certain periodic time-variant behaviours. This extended class of TEGs is called Periodic Time-variant Event Graphs (PTEGs). It is shown that the input-output behaviour of these systems can be described by means of ultimately periodic series in a dioid of formal power series. These series represent transfer functions of PTEGs and are a convenient basis for performance analysis and controller synthesis.

中文翻译：

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dioids 中周期性时变事件图的建模和控制

定时事件图 (TEG) 可以用时不变 (max,+) 线性系统来描述。这种形式主义已被研究用于无决策定时离散事件系统 (DES) 的建模、分析和控制综合，例如在给定逻辑计划下运行的特定制造过程或运输网络。然而，许多应用程序表现出时变行为，无法在标准 TEG 框架中建模。在本文中，我们扩展了 TEG 的类别，以包括某些周期性的时变行为。这种扩展的 TEG 类称为周期性时变事件图 (PTEG)。结果表明，这些系统的输入输出行为可以通过形式幂级数的二元体中的最终周期级数来描述。