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在预定时间窗口内执行任务的离散事件系统模型。其动力学可通过最大加线性对偶不等式（线性动态不等式系统，采用最大加代数的原对偶运算）表示。我们定义了一类称为切换LDI的新模型，允许根据称为调度模式的序列在不同运行模式间切换，每种模式对应一组LDI。本文重点分析当考虑固定且周期性或间歇周期性调度时的SLDI模型。研究表明，SLDI能够建模包括单机器人多产品加工网络在内的广泛实际应用场景，其中每种产品具有不同的加工需求并对应特定运行模式。基于SLDI分析，我们提出算法计算：i. 这些过程的最小与最大周期时间，相较现有方法改进时间复杂度；ii. 包含启动与停机瞬态的机器人完整轨迹。