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

Free access article

Issue		ESAIM: PS Volume 7, 2003


Page(s)		161 - 170
DOI		10.1051/ps:2003007

ESAIM: P&S, March 2003, Vol. 7, pp. 161-170
DOI: 10.1051/ps:2003007

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

M.L. Kleptsyna¹, Alain Le Breton² and M. Viot²

¹ Institute of Information Transmission Problems, Bolshoi Karetnii Per. 19, Moscow 101475, Russia; 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. A-C.Fouilhe-Viot@wanadoo.fr.

(Received September 12, 2002)

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.

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

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

© EDP Sciences, SMAI 2003

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