Volume 7, March 2003
|Page(s)||161 - 170|
|Published online||15 May 2003|
About the linear-quadratic regulator problem under a fractional Brownian perturbation
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.
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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