Control of Linear Stochastic Systems Revisited
The optimal control of a linear stochastic system driven by a Brownian motion with a quadratic cost functional is well known to have a linear feedback control that is identical to the optimal control for the associated deterministic control problem. In this talk the optimal control of a linear system driven by other Gaussian processes, such as an arbitrary fractional Brownian motion, or by non-Gaussian square integrable processes is described. It is shown in these cases that the optimal control is a sum of the well known linear feedback control and the prediction of the response of a system to the future noise. Some other related control problems are also described.
Tyrone Duncan, University of Kansas, USA