# Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation

Marina L. Kleptsyna; Alain Le Breton; Michel Viot

ESAIM: Probability and Statistics (2008)

- Volume: 12, page 94-126
- ISSN: 1292-8100

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topKleptsyna, Marina L., Le Breton, Alain, and Viot, Michel. "Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation." ESAIM: Probability and Statistics 12 (2008): 94-126. <http://eudml.org/doc/250420>.

@article{Kleptsyna2008,

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.
},

author = {Kleptsyna, Marina L., Le Breton, Alain, Viot, Michel},

journal = {ESAIM: Probability and Statistics},

keywords = {Fractional Brownian motion; linear system; optimal control; optimal filtering; quadratic payoff; separation principle; fractional Brownian motion},

language = {eng},

month = {1},

pages = {94-126},

publisher = {EDP Sciences},

title = {Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation},

url = {http://eudml.org/doc/250420},

volume = {12},

year = {2008},

}

TY - JOUR

AU - Kleptsyna, Marina L.

AU - Le Breton, Alain

AU - Viot, Michel

TI - Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation

JO - ESAIM: Probability and Statistics

DA - 2008/1//

PB - EDP Sciences

VL - 12

SP - 94

EP - 126

AB -
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.

LA - eng

KW - Fractional Brownian motion; linear system; optimal control; optimal filtering; quadratic payoff; separation principle; fractional Brownian motion

UR - http://eudml.org/doc/250420

ER -

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