LINEAR-QUADRATIC OPTIMAL CONTROL PROBLEMS FOR MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS

被引：238
|
作者：
Yong, Jiongmin [1 ]
机构：
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 04期
基金：
加拿大自然科学与工程研究理事会; 美国国家科学基金会;
关键词：
mean-field stochastic differential equation; linear-quadratic optimal control; Riccati differential equation; feedback representation; MCKEAN-VLASOV EQUATION; HILBERT-SPACE; EVOLUTION EQUATION; LIMIT; DIFFUSIONS; DYNAMICS;
D O I：
10.1137/120892477
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Linear-quadratic optimal control problems are considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which is a linear mean-field forward-backward stochastic differential equation. Using a decoupling technique, two Riccati differential equations are obtained which are uniquely solvable under certain conditions. Then a feedback representation is obtained for the optimal control.
引用
收藏
页码：2809 / 2838
页数：30
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