On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2010)
ESAIM: Probability and Statistics
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In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.