Social optima in leader-follower mean field linear quadratic control

Jianhui Huang, Bing Chang Wang, Tinghan Xie

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Article number2020056
Pages (from-to)1-31
Number of pages31
JournalESAIM - Control, Optimisation and Calculus of Variations
Publication statusE-pub ahead of print - 1 Mar 2021


  • Forward-backward stochastic differential equation
  • Leader-follower problem
  • Linear quadratic control
  • Social optimality
  • Weakly-coupled stochastic system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


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