Equivalence of multivariable generalized predictive control to receding horizon LQG control

The relationship between multivariable GPC (Generalized Predictive Control) and receding horizon LQG control is not yet fully understood. Incomplete understanding affects adversely the full exploitation of multivariable GPC. In order to gain complete understanding, solution to the multivariable GPC design problem is presented in a stochastic framework. Also for gaining complete understanding, a receding horizon LQG control method is developed. Then the receding horizon LQG is shown to be exactly the same as the GPC solution. After the equality relation between GPC and receding horizon LQG is established, it is now possible to exploit fully multivariable GPC. One and the most important example is that the stability result of receding horizon LQG control can be used for the study of stability property of GPC.