含有时滞的倒向重随机控制系统最大值原理  

Maximum Principle for Backward Doubly Stochastic Control System with Time Delay

作　　者：许洁[1] 吕显瑞[2] XU Jie;LU Xianrui(College of Sciences,Jilin Institute of Chemical Technology,Jilin 132022,Jilin Province,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林化工学院理学院,吉林吉林132022 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2020年第3期493-497,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:15642130);中国汽车产业创新发展联合基金(批准号:11871244);吉林省教育厅“十三五”科学技术项目(批准号:JJKH20200235KJ).

摘　　要：考虑系统状态变量和控制变量均含有时滞的倒向重随机系统的控制问题.通过引入超前倒向重随机微分方程作为其伴随方程,利用经典的凸变分法和对偶技术给出一定条件下的时滞倒向重随机系统的最大值原理.We considered the control problem of the backward doubly stochastic system with time delays in both state variables and the control variables.By introducing the anticipated backward doubly stochastic differential equations as its adjoint equation,using the classical convex variational method and dual technique,we gave the maximum principle for the backward doubly stochastic system with time delay under certain conditions.

关 键 词：重随机微分方程 最大值原理 时滞 最优控制 

分 类 号：O231.3[理学—运筹学与控制论]