不确定数据传输系统时序的最优控制与可靠性

Timing optimal control and reliability of uncertain data transmission systems with interval parameters

研究数据发射时间、传输时间、接收时间不确定的数据传输系统时序的最优控制与可靠性.运用极大–加代数方法,建立不确定数据传输系统的时序演化模型.引入不确定数据传输系统的数据接收时间参变量向量值函数和极大–加线性方程组的非负解,在数据传输时间取自给定区间且发射时间非负的约束条件下,求得数据接收时间的最小值(最早接收时间)和最优解;在数据接收时间限制于给定区间的约束条件下,求得数据发射时间的最大值(最晚发射时间)和最优解.引入不确定数据传输系统的可靠区间,以使数据在这一区间内的任一时刻发射后,均可被按时接收,而免受传输延迟的影响.引入区间参数极大–加线性方程组的容许解区间,给出可靠区间存在性判据,并提供求最大可靠区间的一个有效算法.

This paper presents an investigation of the timing optimal control and timing reliability of data transmission systems of which the launch time,transmission time,and reception time are uncertain.The time series model of uncertain data transmission systems is established by using max-plus algebra.We introduce the parametric vector-valued function of uncertain data transmission systems and the non-negative solution of max-plus linear equations.We determine,on the one hand,the minimum value of the reception time（the earliest reception time） of the data and the corresponding optimal solutions under the constraints for which the transmission time is valued in given intervals and the launch time is non-negative.On the other hand,we establish the maximum value of the launch time（the latest launch time） of the data and the corresponding optimal solutions under the constraints for which the reception time is limited in some intervals.We define reliable intervals of uncertain data transmission systems such that the data can be received within the required time and the influence of transportdelays can be avoided as long as they are launched at any time during such intervals.The tolerance solution intervals of interval systems of max-plus linear equations is introduced to establish the existing criterion of reliable intervals,and an effective algorithm for finding the largest reliable interval is developed.