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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 ,
Alain Le Breton  and
Michel Viot
Marina L. Kleptsyna
Affiliation:
Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans cedex 9, France; [email protected]
Alain Le Breton
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble cedex 9, France; [email protected]
Michel Viot
Affiliation:
Laboratoire de Modélisation et Calcul, Université J. Fourier, BP 53, 38041 Grenoble cedex 9, France; [email protected]
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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.

Keywords

Fractional Brownian motionlinear systemoptimal controloptimal filteringquadratic payoffseparation principle
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 94 - 126
Copyright
© EDP Sciences, SMAI, 2008

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