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On the infinite time horizon linear-quadratic regulator problem undera fractional Brownian perturbation

Published online by Cambridge University Press:  15 November 2005

Marina L. Kleptsyna ,
Alain Le Breton  and
Michel Viot
Marina L. Kleptsyna
Affiliation:
Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans Cedex 9, France; 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
Michel Viot
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble Cedex 9, France; Alain.Le-Breton@imag.fr
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Abstract

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.

Keywords

Fractional Brownian motionlinear systemoptimal controlquadratic payoffinfinite time.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 9 , February 2005 , pp. 185 - 205
Copyright
© EDP Sciences, SMAI, 2005

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