在常规故障下具有四个部件冗余系统解的最优控制  

Optimal Control Problems in A Four-Unit Redundant System with Common-Cause Failure

作　　者：唐慧[1] 周艳巍[2] 赵志欣[3] 

机构地区：[1]白城师范学院数学系,吉林白城137000 [2]延边大学理学院数学系,吉林延边133002 [3]北京控制信息研究所,北京100037

出　　处：《数学的实践与认识》2012年第1期159-164,共6页Mathematics in Practice and Theory

摘　　要：研究了具有常规故障的四个部件冗余可修复系统模型.将一组微分-积分方程描述的模型转化为六维空间的积分方程形式.运用算子理论,证明了此系统非负解的存在唯一性.并且研究了以范数为指标衡量控制标量为标准的最优控制问题.The four-unit redundant system with common-cause was discussed. First, we transformed the system which was described by a group of integrate-differential equation to the Volterra integration equations of six-dimension space. In Banach space, we proved the existence and uniqueness of the non-negative solution of this system with the theory of operator in function analysis and controlled the norm of the scalar index function to measure the standard optimal control problem.

关 键 词：冗余系统 微分-积分方程组 非负解 最优控制 

分 类 号：O232[理学—运筹学与控制论]