Partition of GPC into a State Observer and a State Feedback Controller

In this paper, we transformed the Generalized Predictive Control(GPC) for stochastic I/O models to an optimal output feedback control for state space models of a particular form. The derived output feedback control consists of an optimal state feedback controller and an optimal state observer. It is shown that the optimal state feedback controller is a Receding Horizon Tracking Control(RHTC) and the optimal state observer is a steady state Kalman filter of a special form. The derived output feedback control is shown to be equivalent to GPC through the comparison of the two control values. From the GPC's equivalence to the developed output feedback control, it is shown that the stability properties of GPC are the same as those for RHTC.