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http://hdl.handle.net/10397/93870
Title: | Social optima in leader-follower mean field linear quadratic control | Authors: | Huang, J Wang, BC Xie, T |
Issue Date: | 2021 | Source: | ESAIM. Control, optimisation and calculus of variations, 2021, v. 27, S12 | Abstract: | 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. | Keywords: | Forward-backward stochastic differential equation Leader-follower problem Linear quadratic control Social optimality Weakly-coupled stochastic system |
Publisher: | EDP Sciences | Journal: | ESAIM. Control, optimisation and calculus of variations | ISSN: | 1292-8119 | EISSN: | 1262-3377 | DOI: | 10.1051/cocv/2020056 | Rights: | © EDP Sciences, SMAI 2021 The original publication is available at https://www.esaim-cocv.org/. The following publication Huang, J., Wang, B. C., & Xie, T. (2021). Social optima in leader-follower mean field linear quadratic control. ESAIM: Control, Optimisation and Calculus of Variations, 27, S12 is available at https://doi.org/10.1051/cocv/2020056 |
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