Indefinite Linear Quadratic Mean Field Social Control with Multiplicative Noise

被引：0
作者：
Wang, Bingchang [1 ]
Zhang, Huanshui [1 ]
机构：
[1] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
来源：
2019 IEEE 15TH INTERNATIONAL CONFERENCE ON CONTROL AND AUTOMATION (ICCA) | 2019年
基金：
中国国家自然科学基金;
关键词：
Mean field game; social optimum; forward-backward stochastic differential equation; Riccati equation; MULTIAGENT SYSTEMS; GAMES;
D O I：
暂无
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 studies social optima for linear quadratic mean field control systems with multiplicative noises, where the state and control weights in costs are not limited to be semi-positive definite. We first obtain a set of forward-backward stochastic differential equations (FBSDEs) from variational analysis, and construct a feedback-type control by decoupling the FBSDEs. With the help of solutions to two Riccati equations, we design a set of decentralized control laws, which is further shown to be asymptotically social optimal. Some equivalent conditions are given for uniform stabilization of the systems.
引用
收藏
页码：1056 / 1062
页数：7
相关论文
共 33 条
[1]  
Abou-Kandil H., 2003, SYS CON FDN
[2]  
Arabneydi J, 2015, IEEE DECIS CONTR P, P5308, DOI 10.1109/CDC.2015.7403050
[3]   Linear-Quadratic Mean Field Games [J].
Bensoussan, A. ;
Sung, K. C. J. ;
Yam, S. C. P. ;
Yung, S. P. .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 169 (02) :496-529
[4]  
Bensoussan A, 2013, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-1-4614-8508-7
[5]  
Caines PE., 2017, HDB DYNAMIC GAME THE
[6]   PROBABILISTIC ANALYSIS OF MEAN-FIELD GAMES [J].
Carmona, Rene ;
Delarue, Francois .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (04) :2705-2734
[7]   Mean Field Games Models-A Brief Survey [J].
Gomes, Diogo A. ;
Saude, Joao .
DYNAMIC GAMES AND APPLICATIONS, 2014, 4 (02) :110-154
[8]   TEAM DECISION-THEORY AND INFORMATION STRUCTURES [J].
HO, YC .
PROCEEDINGS OF THE IEEE, 1980, 68 (06) :644-654
[9]   ROBUST MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN GAMES WITH UNKNOWN L2-DISTURBANCE [J].
Huang, Jianhui ;
Huang, Minyi .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2017, 55 (05) :2811-2840
[10]  
Huang MY, 2006, COMMUN INF SYST, V6, P221
1234