Research Article

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

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

^a1 Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans Cedex 9, France; 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

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.

(Received July 19 2004)

(Online publication November 15 2005)

Key Words:

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

Mathematics Subject Classification:

• 60G15;
• 60G44;
• 93E20