A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon

Jianhui Huang, Xun Li, Jiongmin Yong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

52 Citations (Scopus)

Abstract

A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by the discussion of the well-posedness of the LQ problem. The optimal control can be expressed as a linear state feedback involving the state and its mean, through the solutions of two algebraic Riccati equations. The solvability of such kind of Riccati equations is investigated by means of semi-definite programming method.
Original languageEnglish
Pages (from-to)97-139
Number of pages43
JournalMathematical Control and Related Fields
Volume5
Issue number1
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Linear-quadratic optimal control
  • Mean-field stochastic differential equation
  • MF-stabilizability
  • Riccati equation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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