文章基本信息

标题：Necessary and Sufficient Solution to Optimal Control for Linear Continuous Time Mean-field System * * This work is supported by the National Natural Science Foundation of China under Grants 61120106011, 61573221, 61633014.
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作者：Qingyuan Qi ; Huanshui Zhang
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2017
卷号：50
期号：1
页码：1495-1501
DOI：10.1016/j.ifacol.2017.08.298
语种：English
出版社：Elsevier
摘要：AbstractDifferent from previous works, this paper will provide the necessary and sufficient (essential) solution to linear quadratic (LQ) optimal control problem for continuous-time mean-field systems. Firstly by applying the Maximum Principle developed in this paper, the necessary and sufficient solvability condition of the finite horizon mean-field optimal control problem is presented in an explicit expression form (in analytical form) for the first time, which is completely different from the operator-type conditions obtained in previous works. Secondly, we explore the analytical solution to the forward and backward stochastic differential equation (FBSDE) of the mean-field optimal control problem. Accordingly, the optimal controller, in terms of system state and its expectation, is designed via a coupled Riccati equation. It is very interesting to show that the coupled Riccati equation is derived from the solution to the FBSDE, which has the similarity with the case of standard optimal control.
关键词：KeywordsMean-field LQ controlmaximum principleRiccati equationoptimal controller