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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (10): 1-10.doi: 10.6040/j.issn.1671-9352.9.2021.012

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正倒向随机最优控制问题的最大值原理:完全信息和部分信息

吴臻1*,王光臣2,李敏1   

  1. 1.山东大学数学学院, 山东 济南 250100;2.山东大学控制科学与工程学院, 山东 济南 250061
  • 发布日期:2021-09-28
  • 作者简介:吴臻(1971— ), 男, 博士, 教授, 博士生导师, 研究方向为随机控制、 正倒向随机微分方程、 数理金融. E-mail:wuzhen@sdu.edu.cn*通信作者
  • 基金资助:
    国家自然科学基金重点资助项目(11831010);中港合作项目(61961160732);国家自然科学基金杰出青年科学基金资助项目(61925306);山东省自然基金重大项目(ZR2019ZD42,ZR2020ZD24);山东省泰山学者攀登计划(TSPD20210302)

Maximum principle for optimal control of forward-backward stochastic system: full information and partial information

WU Zhen1*, WANG Guang-chen2, LI Min1   

  1. 1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
    2. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China
  • Published:2021-09-28

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摘要： 本文是一篇关于正倒向随机最优控制问题研究进展的综述论文。近30年来,正倒向随机控制系统的各种理论与应用研究得到了迅猛发展,取得了大量原创性科研成果,吸引了大批国际同行跟进研究。限于论文篇幅和作者意图,本文仅仅聚焦于正倒向随机最优控制问题的最大值原理这一主题,概述其最新研究进展及其在求解线性二次最优控制问题中的简单应用。

关键词: 正倒向随机系统, 一般最大值原理, 最优滤波, 倒向分离方法, 线性二次控制

Abstract: This paper reviews some progresses on forward-backward stochastic control system. In the past 30 years, various theories and applications of forward-backward stochastic control system have been developed rapidly and a large number of original scientific research results have been obtained, which have attracted many international peers to follow-up research. Limited to the length of this paper and the authors emphasis, this paper only focuses on maximum principle for optimal control of forward-backward stochastic system, and summarizes its latest research progress and application in solving linear quadratic optimal control problem.

Key words: forward-backward stochastic system, general maximum principle, optimal filtering, backward separation approach, linear-quadratic control

中图分类号: 

  • O211
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