| Issue |
ESAIM: PS
Volume 7, March 2003
|
|
|---|---|---|
| Page(s) | 161 - 170 | |
| DOI | https://doi.org/10.1051/ps:2003007 | |
| Published online | 15 May 2003 | |
About the linear-quadratic regulator problem under a fractional Brownian perturbation
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:
12
September
2002
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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