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

Abstract

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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.

How to cite

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Kleptsyna, 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 -

References

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  12. M.L. Kleptsyna, A. Le Breton and M. Viot, On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation. ESAIM: PS9 (2005) 185–205.  Zbl1136.93463
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