This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a “worst case” disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions.
Keywords: Mean field game, model uncertainty, linear quadratic control, social optimality, forward-backward stochastic differential equation
@article{COCV_2021__27_1_A22_0,
author = {Xie, Tinghan and Wang, Bing-Chang and Huang, Jianhui},
title = {Robust linear quadratic mean field social control: {A} direct approach},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021021},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021021/}
}
TY - JOUR AU - Xie, Tinghan AU - Wang, Bing-Chang AU - Huang, Jianhui TI - Robust linear quadratic mean field social control: A direct approach JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021021/ DO - 10.1051/cocv/2021021 LA - en ID - COCV_2021__27_1_A22_0 ER -
%0 Journal Article %A Xie, Tinghan %A Wang, Bing-Chang %A Huang, Jianhui %T Robust linear quadratic mean field social control: A direct approach %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021021/ %R 10.1051/cocv/2021021 %G en %F COCV_2021__27_1_A22_0
Xie, Tinghan; Wang, Bing-Chang; Huang, Jianhui. Robust linear quadratic mean field social control: A direct approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 20. doi: 10.1051/cocv/2021021
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Cité par Sources :
The first author acknowledges the financial support from: P0008686, P0031044. The second author acknowledges the support from: NNSF of China (61773241), the Youth Innovation Group Project of Shandong University (2020QNQT016). The third author acknowledges the support from: RGC 153005/14P, 153275/16P, P0030808. The authors also acknowledge the support from: The PolyU-SDU Joint Research Centre on Financial Mathematics.
