Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon
Wang, Bing-Chang1; Huang, Jianhui2; Zhang, Ji-Feng3,4
AbstractThis article studies social optimal control of mean field linear-quadratic-Gaussian models with uncertainty. Specially, the uncertainty is represented by an uncertain drift, which is common for all agents. A robust optimization approach is applied by assuming all agents treat the uncertain drift as an adversarial player. In our model, both dynamics and costs of agents are coupled by mean field terms, and both finite- and infinite-time horizon cases are considered. By examining social functional variation and exploiting person-by-person optimality principle, we construct an auxiliary control problem for the generic agent via a class of forward-backward stochastic differential equation system. By solving the auxiliary problem and constructing consistent mean field approximation, a set of decentralized control strategies is designed and shown to be asymptotically optimal.
KeywordMathematical model Games Robustness Uncertainty Optimal control Stochastic processes Differential equations Forward-backward stochastic differential equation (FBSDE) linear quadratic optimal control mean field control model uncertainty social functional variation
Indexed BySCI
Funding ProjectNational Key R&D Program of China[2018YFA0703800] ; National Natural Science Foundation of China[61773241] ; National Natural Science Foundation of China[61877057] ; RGC[P0030808] ; RGC[P0005158] ; Youth Innovation Group Project of Shandong University[2020QNQT016] ; PolyU-SDU Joint Research Center on Financial Mathematics
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000634485900006
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Document Type期刊论文
Corresponding AuthorZhang, Ji-Feng
Affiliation1.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Peoples R China
2.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong 999077, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100149, Peoples R China
Recommended Citation
GB/T 7714
Wang, Bing-Chang,Huang, Jianhui,Zhang, Ji-Feng. Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2021,66(4):1529-1544.
APA Wang, Bing-Chang,Huang, Jianhui,&Zhang, Ji-Feng.(2021).Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,66(4),1529-1544.
MLA Wang, Bing-Chang,et al."Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 66.4(2021):1529-1544.
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