Optimal nominal dual control for discrete-time linear-quadratic Gaussian problems with unknown parameters

The dual control for a class of discrete-time linear-quadratic Gaussian problems with unknown parameters is studied in this paper. To achieve an optimality in dual control, a control law must possess a property of active learning. The best possible (partial) closed-loop feedback control law is derived in this paper by exploring the future nominal posterior probabilities, thus taking into account the effect of future learning when constructing an optimal nominal control law.