P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

翻译：P时间事件图是适用于建模任务必须在预定义时间窗口内执行过程的离散事件系统。其动力学可通过极大-加线性-对偶不等式（LDI）表示，即极大-加代数中原始运算和对偶运算下的线性动力不等式系统。我们定义了一类称为切换LDI（SLDI）的新模型，该类模型允许根据称为调度的模式序列在不同操作模式间切换，每种模式对应一组LDI。本文重点分析当考虑调度固定且呈周期性或间歇周期性时SLDI的性质。研究表明，SLDI可建模包括单机器人多产品加工网络在内的广泛应用场景，其中每种产品具有不同的加工需求且对应特定操作模式。基于SLDI分析，我们提出算法计算：i. 这些过程的最小和最大周期时间，相较于现有方法降低了时间复杂度；ii. 包含启动和停机暂态的机器人完整轨迹。