Control of some linear stochastic systems with a fractional Brownian motion

In this paper a control problem for a linear stochastic system driven by a fractional Brownian motion with a cost functional that is quadratic in the state and the control is considered. An optimal control is given explicitly using fractional calculus and the control is shown to depend on the prediction of the fractional Brownian motion as well as the usual linear feedback control for the linear-quadratic control problem.

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