标题：A Complete Solution to Mean Field Linear Quadratic Control
作者机构：[Wang, Bing-Chang ] School of Control Science and Engineering, Shandong University, Jinan; 250061, China
会议名称：37th Chinese Control Conference, CCC 2018
会议日期：25 July 2018 through 27 July 2018
来源：Chinese Control Conference, CCC
关键词：Forward-backward stochastic differential equation; Mean field game; Open-loop control; Social optimality
摘要：This paper studies uniform stabilization and social optimality for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the finite horizon case, we first obtain a set of forward-backward stochastic differential equations (FBSDE) from the analysis of the social cost variation, and then design a feedback-type control by decoupling the FBSDE. The set of decentralized control laws is shown to have asymptotic social optimality. For the infinite horizon case, we design an asymptotically social optimal decentralized control using solutions of two Riccati equations. Two equivalent conditions are further given for uniform stabilization of the systems in different cases. Finally, we show that such decentralized control is a representation of the feedback control in previous works. © 2018 Technical Committee on Control Theory, Chinese Association of Automation.