Linear-Quadratic Fractional Gaussian Control

In this paper a control problem for a linear stochastic system driven by a noise process that is an arbitrary zero mean, square integrable stochastic process with continuous sample paths and a cost functional that is quadratic in the system state and the control is solved. An optimal control is give...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2013-01, Vol.51 (6), p.4504-4519
Main Authors: Duncan, Tyrone E., Pasik-Duncan, Bozenna
Format: Article
Language:English
Subjects:
Brownian motion
Calculus
Hilbert space
Noise
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Summary:In this paper a control problem for a linear stochastic system driven by a noise process that is an arbitrary zero mean, square integrable stochastic process with continuous sample paths and a cost functional that is quadratic in the system state and the control is solved. An optimal control is given explicitly as the sum of the well-known linear feedback control for the associated deterministic linear-quadratic control problem and the prediction of the response of a system to the future noise process. The optimal cost is also given. The special case of a noise process that is an arbitrary standard fractional Brownian motion is noted explicitly with an explicit expression for the prediction of the future response of a system to the noise process that is used the optimal control. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/120877283