Volume 27, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Number of page(s)||31|
|Published online||01 March 2021|
Social optima in leader-follower mean field linear quadratic control*
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: 18 August 2020
This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the social cost. Specifically, for any strategy provided first by the leader, the followers would like to choose a strategy to minimize social cost functional. Using variational analysis and person-by-person optimality, we construct two auxiliary control problems. By solving sequentially, the auxiliary control problems with consistent mean field approximations, we can obtain a set of decentralized social optimality strategy with help of a class of forward-backward consistency systems. The relevant Stackelberg equilibrium is further proved under some proper conditions.
Mathematics Subject Classification: 91A12 / 91A23 / 91A25 / 93E03 / 93E20
Key words: Leader-follower problem / weakly-coupled stochastic system / linear quadratic control / social optimality / forward-backward stochastic differential equation
The first author acknowledges the financial support from: RGC 153005/14P, 153275/16P, P0030808; the second author acknowledges the support from: NNSF of China: 61773241; the third author acknowledges the support from: P0008686, P0031044; the authors also acknowledge the support from: the PolyU-SDU Joint Research Centre on Financial Mathematics.
© EDP Sciences, SMAI 2021
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