Discrete time mean-field stochastic linear-quadratic optimal control problems

Robert Elliott, Xun Li, Yuan Hua Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review

133 Citations (Scopus)


This paper firstly presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Secondly, the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method. Thirdly, by introducing several sequences of bounded linear operators, the problem is formulated as an operator stochastic linear-quadratic optimal control problem. By the kernel-range decomposition representation of the expectation operator and its pseudo-inverse, the optimal control is derived using solutions to two algebraic Riccati difference equations. Finally, by completing the square, the two Riccati equations and the optimal control are also obtained.
Original languageEnglish
Pages (from-to)3222-3233
Number of pages12
Issue number11
Publication statusPublished - 1 Nov 2013


  • Mean-field theory
  • Riccati difference equation
  • Stochastic linear-quadratic optimal control problem

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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