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.
Mots-clés : 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},
pages = {161--170},
publisher = {EDP-Sciences},
volume = {7},
year = {2003},
doi = {10.1051/ps:2003007},
mrnumber = {1956077},
zbl = {1030.93059},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2003007/}
}
TY - JOUR AU - Kleptsyna, M. L. AU - Breton, Alain Le AU - Viot, M. TI - About the linear-quadratic regulator problem under a fractional brownian perturbation JO - ESAIM: Probability and Statistics PY - 2003 SP - 161 EP - 170 VL - 7 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2003007/ DO - 10.1051/ps:2003007 LA - en ID - PS_2003__7__161_0 ER -
%0 Journal Article %A Kleptsyna, M. L. %A Breton, Alain Le %A Viot, M. %T About the linear-quadratic regulator problem under a fractional brownian perturbation %J ESAIM: Probability and Statistics %D 2003 %P 161-170 %V 7 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2003007/ %R 10.1051/ps:2003007 %G en %F 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, Tome 7 (2003), pp. 161-170. doi : 10.1051/ps:2003007. http://archive.numdam.org/articles/10.1051/ps:2003007/
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