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.