条件平均场随机微分方程的最优控制问题  

Optimal Control Problem of Conditional Mean-Field Stochastic Differential Equations

作　　者：吴霜[1] WU Shuang(Department of Applied Mathematics,China University of Petroleum,Qingdao 266580,Shandong,China)

机构地区：[1]中国石油大学(华东)应用数学系,山东青岛266580

出　　处：《数学年刊（A辑）》2021年第1期75-88,共14页Chinese Annals of Mathematics

摘　　要：作者研究了一个条件平均场随机微分方程的最优控制问题.这种方程和某些部分信息下的随机最优控制问题有关,并且可以看做是平均场随机微分方程的推广.作者以庞特里雅金最大值原理的形式给出最优控制满足的必要和充分条件.此外,文中给出一个线性二次最优控制问题来说明理论结果的应用.In this paper the author studies a class of optimal control problem,where the state dynamics are described as some conditional mean-field stochastic differential equations.This kind of equations is related to some stochastic optimal control problems under partial information and can be seen as an extension of mean-field stochastic differential equations.The author deduces the necessary condition as well as sufficient condition for the optimality in the form of Pontryagin’s maximum principle.Moreover,a linear quadratic optimal control problem is discussed to explain the theoretical application.

关 键 词：条件平均场随机微分方程 随机最大值原理 倒向随机微分方程 线性二次最优控制 黎卡堤方程 

分 类 号：O225[理学—运筹学与控制论] O231.3[理学—数学]