多步反馈控制作用下的离散事件动态系统的周期计算

Computation of Period for Discrete Event Dynamic Systems with Multi-State Feedback Control

我们考察极大代数意义下的线性离散事件动态系统（ＤＥＤＳ）．在多步反馈控制作用下，熟知求系统运行的周期就是要求有ｒｌ个顶点的图的关键回路．本文重构一个只有ｒ个顶点的有向赋权图Ｇ（Ｆ），证明求系统的周期等价于求Ｇ（Ｆ）的关键回路，从而将一个求ｒｌ个顶点的图的关键回路问题简化为求一个只有ｒ个顶点的图的关键回路问题．

We consider the linear(in the sense of Max -algebra)discrete event dynamic systems with multi stage feedback control. It is well-known that in order to find the period of the system we need to seek for the criti cal circuits of a diagraph with rl vertices.In this paper,we reconstruct a weighted multigraph G(F) with r vertices and show that the period of the system can be obtained from the critical circuits of G(F).Thus,the problem of seeking for critical circuits of a diagraph with lr vertices is simplified to the one with r vertices .