Discrete time mean-field stochastic linear-quadratic optimal control problems

被引：158
作者：
Elliott, Robert [1 ,2 ]
Li, Xun [3 ]
Ni, Yuan-Hua [4 ,5 ]
机构：
[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia
[2] Univ Calgary, Haskayne Sch Business, Calgary, AB, Canada
[3] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
[4] Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300160, Peoples R China
[5] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
来源：
AUTOMATICA | 2013年 / 49卷 / 11期
基金：
加拿大自然科学与工程研究理事会; 中国国家自然科学基金;
关键词：
Stochastic linear-quadratic optimal control problem; Mean-field theory; Riccati difference equation; MCKEAN-VLASOV EQUATION; MULTIAGENT SYSTEMS; DIFFERENTIAL-EQUATIONS; H-2/H-INFINITY CONTROL; NASH EQUILIBRIA; HILBERT-SPACE; GAMES; DYNAMICS; BEHAVIOR; STATE;
D O I：
10.1016/j.automatica.2013.08.017
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3222 / 3233
页数：12
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