In this paper we solve the basic fractional analogue of the classical linear-quadratic gaussian regulator problem in continuous time. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes a quadratic performance criterion.

Classification: 93E20, 60G15, 60G44

Keywords: fractional brownian motion, linear system, optimal control, quadratic payoff

@article{PS_2003__7__161_0, author = {Kleptsyna, M. L. and Breton, Alain Le and Viot, M.}, title = {About the linear-quadratic regulator problem under a fractional brownian perturbation}, journal = {ESAIM: Probability and Statistics}, publisher = {EDP-Sciences}, volume = {7}, year = {2003}, pages = {161-170}, doi = {10.1051/ps:2003007}, zbl = {1030.93059}, mrnumber = {1956077}, language = {en}, url = {http://www.numdam.org/item/PS_2003__7__161_0} }

Kleptsyna, M. L.; Breton, Alain Le; Viot, M. About the linear-quadratic regulator problem under a fractional brownian perturbation. ESAIM: Probability and Statistics, Volume 7 (2003) , pp. 161-170. doi : 10.1051/ps:2003007. http://www.numdam.org/item/PS_2003__7__161_0/

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