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J4 ›› 2013, Vol. 48 ›› Issue (09): 90-95.

• 论文 • 上一篇    下一篇

随机H2/H∞控制的最大值原理方法

孙启良,张启侠*   

  1. 济南大学数学科学学院, 山东 济南 250022
  • 收稿日期:2013-03-13 出版日期:2013-09-20 发布日期:2013-09-25
  • 通讯作者: 张启侠(1985- ), 女,讲师,博士,研究方向为电优控制.Email: zhangqixia11@163.com
  • 作者简介:孙启良(1980- ),男,讲师,硕士,研究方向为最优控制,机器学习.Email: ss-sunql@ujn.edu.cn
  • 基金资助:

    国家自然科学青年基金资助项目(11101242);济南大学博士基金资助项目(XBS1213)

A maximum principle approach for stochastic H2/H∞ control

SUN Qi-liang, ZHANG Qi-xia*   

  1. School of Mathematical Sciences, University of Jinan, Jinan 250022, Shandong, China
  • Received:2013-03-13 Online:2013-09-20 Published:2013-09-25

摘要:

利用非零和微分对策的最大值原理求解噪声依赖于(x,u,v)的随机H2/H∞控制问题,提出了该控制问题存在惟一解的一个充分必要条件,即其对应的无控制随机扰动系统的L2收益小于或等于γ。在该控制问题有解时,通过一个正倒向随机微分方程给出该控制问题的惟一解。

关键词: 最大值原理;随机H2/H∞控制;正倒向随机微分方程;Riccati方程

Abstract:

 The maximum principle for nonzero-sum stochastic differential games was applied to solve the stochastic H2/H∞ control problem with (x,u,v)-dependent noise. It is shown that the existence of a unique solution to the control problem is equivalent to the corresponding uncontrolled perturbed system to have L2-gain less than or equal to γ and the resulting solution is characterized by the solution of an uncontrolled forward backward stochastic differential equation (FBSDE).

Key words: the maximum principle; stochastic H2/H∞ control; forward backward stochastic differential equation (FBSDE); Riccati equation

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