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Issue ESAIM: P&S Volume 9, 2005 Page(s) 185 - 205 DOI 10.1051/ps:2005008

ESAIM: P&S, May 2005, Vol. 9, pp. 185-205
DOI: 10.1051/ps:2005008

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

Marina L. Kleptsyna¹, Alain Le Breton² and Michel Viot<sup>2

1</sup>  Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans Cedex 9, France; marina.kleptsyna@univ-lemans.fr
²  Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble Cedex 9, France; Alain.Le-Breton@imag.fr

(Received July 19, 2004.)

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.

Mathematics Subject Classification. 60G15, 60G44, 93E20.

Key words: Fractional Brownian motion, linear system, optimal control, quadratic payoff, infinite time.


© EDP Sciences, SMAI 2005

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