| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 20 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2021021 | |
| Published online | 26 March 2021 | |
Robust linear quadratic mean field social control: A direct approach*
1
Department of Applied Mathematics, The Hong Kong Polytechnic University,
Hong Kong, PR China.
2
School of Control Science and Engineering, Shandong University,
Jinan, PR China.
** Corresponding author: bcwang@sdu.edu.cn
Received:
7
December
2020
Accepted:
12
February
2021
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.
Mathematics Subject Classification: 49N10 / 49N70 / 91A12 / 93E03
Key words: Mean field game / model uncertainty / linear quadratic control / social optimality / forward-backward stochastic differential equation
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.
© EDP Sciences, SMAI 2021
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