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

中文关键词  离散事件动态系统  极大代数  关键回路  周期  多步反馈控制

英文关键词  discrete event dynamic systems  max-algebra  critical circuit  period  multi-stage feedback control laws

中文摘要

      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。

英文摘要

      We consider the linear (in the sense of Max-algebra) discrete event dynamic systems with multi-state feedback control. It is well-known that in order to find the period of the system we need to seek for the critical 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 G vertices is simplified to the one with r vertices.