Research Article

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

Kleptsyna, M. L.^a1, Le Breton, Alain^a2 and Viot, M.^a2

^a1 Institute of Information Transmission Problems, Bolshoi Karetnii Per. 19, Moscow 101475, Russia; Marina.Kleptsyna@univ-lemans.fr.

^a2 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.

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.

(Received September 12 2002)

(Online publication May 15 2003)

Key Words:

• Fractional Brownian motion;
• linear system;
• optimal control;
• quadratic payoff.

Mathematics Subject Classification:

• 93E20;
• 60G15;
• 60G44