Stochastic linear-quadratic control for systems with a fractional Brownian motion

In this paper a control problem for a linear stochastic system with a fractional Brownian motion and a cost functional that is quadratic in the state and the control is solved. An optimal control is given explicitly using fractional calculus and the control is shown to depend on a prediction of the future fractional Brownian motion and the well known linear feedback control for the deterministic linear-quadratic control problem. It is noted that the methods to obtain an optimal control extend to other noise processes with continuous sample paths.