Backward linear quadratic stochastic optimal control problems and nonzero sum differential games
作者单位：School of Mathematics and Statistics Shandong University at Weihai
会议名称：《第25届中国控制与决策会议》
主办单位：IEEE;NE Univ;IEEE Ind Elect Chapter;IEEE Harbin Sect Control Syst Soc Chapter;Guizhou Univ;IEEE Control Syst Soc;Syst Engn Soc China;Chinese Assoc Artificial Intelligence;Chinese Assoc Automat;Tech Comm Control Theory;Chinese Assoc Aeronaut;Automat Control Soc;Chinese Assoc Syst Simulat;Simulat Methods & Modeling Soc;Intelligent Control & Management Soc
会议日期：2013年
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学]
关 键 词：Mean-field forward-backward stochastic differential equations stochastic optimal control nonzero sum differential games.
摘 要：In R. Buckdahn, Li, Peng [6], the authors obtained mean-field backward stochastic Differential equations （BSDEs） in a natural way as a limit of some highly dimensional system of forward and backward SDEs, corresponding to a great number of particles. In this paper, firstly, we prove that there exists a unique solution of fully coupled MF-FBSDE. Then we use the solutions of mean-field forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic optimal control problem and the open-loop Nash equilibrium point of nonzero sum differential games.