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MCRF

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.

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