This paper is about control sequences design for Discrete Event Systems (DES) modeled with Time Petri nets (TPN) including a set of temporal specifications. Petri nets are known as efficient mathematical and graphical models that are widely used to describe distributed DES including choices, synchronizations and parallelisms. The domains of application include but are not restricted to manufacturing systems, computer science and transportation networks. Incorporating the time in the model is important to consider many control problems such as scheduling and planning. This paper solves some control issues in timed context and uncertain environments that include unexpected events modeled with uncontrollable transitions. To deal with such uncertainties, we propose first to build an Approximated Timed Reachability Graph that includes the time specifications and model all feasible timed trajectories at a given accuracy under earliest firing policy. Then, this graph is used to search optimal paths by using an approach based on Markov Decision Processes that encode the environment uncertainties. Such optimal paths lead to near-optimal solutions for the TPN. Several simulations illustrate the benefit of the proposed method from the performance and computational points of view.

中文翻译：

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离散事件系统鲁棒控制的近似定时可达图

本文是关于使用时间 Petri 网 (TPN) 建模的离散事件系统 (DES) 的控制序列设计，包括一组时间规范。Petri 网被称为高效的数学和图形模型，广泛用于描述分布式 DES，包括选择、同步和并行。应用领域包括但不限于制造系统、计算机科学和运输网络。在模型中加入时间对于考虑调度和计划等许多控制问题很重要。本文解决了定时上下文和不确定环境中的一些控制问题，其中包括以不可控制的转换建模的意外事件。为了应对这种不确定性，我们首先建议构建一个近似定时可达图，其中包括时间规范，并在最早触发策略下以给定精度对所有可行的定时轨迹进行建模。然后，该图用于通过使用基于对环境不确定性进行编码的马尔可夫决策过程的方法来搜索最佳路径。这种最优路径导致 TPN 接近最优解。几个模拟从性能和计算的角度说明了所提出的方法的好处。