A partial information linear-quadratic optimal control problem of backward stochastic differential equation with its applications

作     者：Pengyan HUANG Guangchen WANG Huanjun ZHANG Pengyan HUANG;Guangchen WANG;Huanjun ZHANG

作者机构：School of Control Science and Engineering Shandong University 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2020年第63卷第9期

页      面：188-200页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：supported in part by National Natural Science Foundation of China (Grant Nos.11371228 61821004 61633015) 

主　　题：backward stochastic differential equation feedback representation linear-quadratic optimal control mean-field optimal filter 

摘      要：In this paper, we investigate a kind of partial information linear-quadratic optimal control problem driven by a backward stochastic differential equation, where the state equation and the cost functional contain diffusion terms. Using maximum principle, we derive the corresponding Hamiltonian system, which is a conditional mean-field forward-backward stochastic differential equation. By the backward separation approach and the filtering technique, we get two Riccati equations, and a backward and a forward optimal filtering equations. Then a feedback form of optimal control is obtained. We also extend the control problem to the case of mean-field backward stochastic differential equation under partial information. A corresponding feedback form of optimal control is also obtained.