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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; [email protected].
Alain Le Breton
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP. 53, 38041 Grenoble Cedex 9, France; [email protected]. [email protected].
M. Viot
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP. 53, 38041 Grenoble Cedex 9, France; [email protected]. [email protected].
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Abstract

In this paper we solve the basic fractionalanalogue of the classical linear-quadratic Gaussianregulator problem in continuous time. For a completelyobservable controlled linear system driven by a fractionalBrownian motion, we describe explicitely the optimal controlpolicy 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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References

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