Volume 9, June 2005
|Page(s)||185 - 205|
|Published online||15 November 2005|
On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
Laboratoire de Statistique
et Processus, Université du Maine, av. Olivier Messiaen, 72085
Le Mans Cedex 9, France; email@example.com
2 Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble Cedex 9, France; Alain.Le-Breton@imag.fr
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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