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Separation principle in the fractional Gaussianlinear-quadratic regulator problem withpartial observation

Published online by Cambridge University Press:  23 January 2008

Marina L. Kleptsyna
Affiliation:
Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans cedex 9, France; Marina.Kleptsyna@univ-lemans.fr
Alain Le Breton
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble cedex 9, France; Alain.Le-Breton@imag.fr
Michel Viot
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble cedex 9, France; Alain.Le-Breton@imag.fr
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Abstract

In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal filtering of the unobservable state and optimal control of the filtered state. Both finite and infinite time horizon problems are investigated.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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