Linear quadratic mean field game with control input constraint ?

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23 Citations (Scopus)


In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset Γ of full space ?m. The decentralized strategies and consistency condition are represented by a class of mean-field forward-backward stochastic differential equation (MF-FBSDE) with projection operators on Γ. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related ? -Nash equilibrium property is also verified.
Original languageEnglish
Pages (from-to)901-919
Number of pages19
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number2
Publication statusPublished - 1 Apr 2018


  • ? -Nash equilibrium
  • Linear-quadratic constrained control
  • Mean-field forward-backward stochastic differential equation (MF-FBSDE)
  • Monotonic condition
  • Projection

ASJC Scopus subject areas

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


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