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

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.