# American Institute of Mathematical Sciences

March  2015, 5(1): 97-139. doi: 10.3934/mcrf.2015.5.97

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

 1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816

Received  July 2013 Revised  November 2013 Published  January 2015

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