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About the linear-quadratic regulator problem under a fractional Brownian perturbation

Published online by Cambridge University Press:  15 May 2003

M. L. Kleptsyna ,
Alain Le Breton  and
M. Viot
M. L. Kleptsyna
Affiliation:
Institute of Information Transmission Problems, Bolshoi Karetnii Per. 19, Moscow 101475, Russia; Marina.Kleptsyna@univ-lemans.fr.
Alain Le Breton
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP. 53, 38041 Grenoble Cedex 9, France; Alain.Le-Breton@imag.fr. A-C.Fouilhe-Viot@wanadoo.fr.
M. Viot
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP. 53, 38041 Grenoble Cedex 9, France; Alain.Le-Breton@imag.fr. A-C.Fouilhe-Viot@wanadoo.fr.
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Abstract

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.

Keywords

Fractional Brownian motionlinear systemoptimal controlquadratic payoff.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 161 - 170
Copyright
© EDP Sciences, SMAI, 2003

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