Volume 27, 2021
|Number of page(s)||19|
|Published online||26 March 2021|
Robust linear quadratic mean field social control: A direct approach*
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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.