SOCIAL OPTIMA IN MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN MODELS WITH MARKOV JUMP PARAMETERS

doi:10.1137/15M104178X

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	SOCIAL OPTIMA IN MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN MODELS WITH MARKOV JUMP PARAMETERS
	Wang, Bing-Chang 1; Zhang, Ji-Feng2,3
	2017
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	55 期号:1 页码:429-456
摘要	This paper investigates social optima of mean field linear-quadratic-Gaussian (LQG) control models with Markov jump parameters. The common objective of the agents is to minimize a social cost-the cost average of the whole society. In the cost functions there are coupled mean field terms. First, we consider the centralized case and get a parameterized equation of mean field effect. Then, we design a set of distributed strategies by solving a limiting optimal control problem in an augmented state space subject to the consistency requirement for mean field approximation. It is shown that the set of distributed strategies is asymptotically team-optimal, and the asymptotically optimal social cost value can be obtained explicitly. The optimal social average cost is compared with the optimal individual cost in mean field games by virtue of the explicit expressions, and the difference is further illustrated by a numerical example.
关键词	mean field model team decision problem social optimum LQG control Markov jump parameter
DOI	10.1137/15M104178X
语种	英语
资助项目	National Natural Science Foundation of Chinaunder[61403233] ; National Natural Science Foundation of Chinaunder[61227902] ; National Natural Science Foundation of Chinaunder[61503218] ; National Natural Science Foundation of Chinaunder[61633014] ; National Key Basic Research Program of China (973 Program)[2014CB845301]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000396679400017
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24850
专题	系统科学研究所
通讯作者	Wang, Bing-Chang
作者单位	1.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China 2.Chinese Acad Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Wang, Bing-Chang,Zhang, Ji-Feng. SOCIAL OPTIMA IN MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN MODELS WITH MARKOV JUMP PARAMETERS[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2017,55(1):429-456.
APA	Wang, Bing-Chang,&Zhang, Ji-Feng.(2017).SOCIAL OPTIMA IN MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN MODELS WITH MARKOV JUMP PARAMETERS.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,55(1),429-456.
MLA	Wang, Bing-Chang,et al."SOCIAL OPTIMA IN MEAN FIELD LINEAR-QUADRATIC-GAUSSIAN MODELS WITH MARKOV JUMP PARAMETERS".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 55.1(2017):429-456.