On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation

Marina L. Kleptsyna; Alain Le Breton; Michel Viot

ESAIM: Probability and Statistics (2010)

  • Volume: 9, page 185-205
  • ISSN: 1292-8100

Abstract

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In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.

How to cite

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Kleptsyna, Marina L., Le Breton, Alain, and Viot, Michel. "On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation." ESAIM: Probability and Statistics 9 (2010): 185-205. <http://eudml.org/doc/104329>.

@article{Kleptsyna2010,
abstract = { In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion. },
author = {Kleptsyna, Marina L., Le Breton, Alain, Viot, Michel},
journal = {ESAIM: Probability and Statistics},
keywords = {Fractional Brownian motion; linear system; optimal control; quadratic payoff; infinite time.; optimal control; infinite time},
language = {eng},
month = {3},
pages = {185-205},
publisher = {EDP Sciences},
title = {On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation},
url = {http://eudml.org/doc/104329},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Kleptsyna, Marina L.
AU - Le Breton, Alain
AU - Viot, Michel
TI - On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 185
EP - 205
AB - In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
LA - eng
KW - Fractional Brownian motion; linear system; optimal control; quadratic payoff; infinite time.; optimal control; infinite time
UR - http://eudml.org/doc/104329
ER -

References

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