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Linear-quadratic fractional Gaussian control
Duncan, Tyrone E. Pasik-Duncan, Bozenna
Duncan, Tyrone E.
Pasik-Duncan, Bozenna
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Abstract
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/120877283.
Date
2013-01-01
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Society for Industrial and Applied Mathematics
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Keywords
linear-quadratic control with general noise processes, linear-quadratic Gaussian control, control of linear systems with fractional Brownian motions, control of continuous time linear systems
Citation
Duncan, Tyrone E. "Linear-quadratic fractional Gaussian control." SIAM J. Control Optim. (2013) 51, 6. 4504-4519. http://www.dx.doi.org/10.1137/120877283.