A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon
Jianhui Huang Xun Li Jiongmin Yong
Mathematical Control & Related Fields 2015, 5(1): 97-139 doi: 10.3934/mcrf.2015.5.97
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.
keywords: MF-stabilizability Riccati equation. Mean-field stochastic differential equation linear-quadratic optimal control

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