Document ESAIM: PS, 2008, Vol. 12, p. 94-126
DOI: 10.1051/ps:2007046
Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation
Marina L. Kleptsyna1, Alain Le Breton2 and Michel Viot21 Laboratoire de Statistique et Processus, Université du Maine, av. Olivier Messiaen, 72085 Le Mans cedex 9, France; 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
Received July 21, 2006. Revised January 8, 2007. Published online 23 January 2008
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.
Mathematics Subject Classification. 93E11, 93E20. 60G15, 60G44
Key words: Fractional Brownian motion, linear system, optimal control, optimal filtering, quadratic payoff, separation principle
© EDP Sciences, SMAI 2008