Multivariable linear quadratic generalized predictive control

The multivariable generalized predictive control (GPC) law is derived in a stochastic setting which closely follows the usual polynomial solution of the LQG problem. The assumptions which must be made to ensure a GPC type of control law emerges are clear from the analysis which provides insights into the relationship between LQG and GPC control. The form of the single degree-of-freedom control law obtained closely parallels the GPC solution but ensures closed loop stability. The solution of the multi-step cost-function problem is shown to include an LQG controller which must be implemented for the actual feedback system and a set of controllers which are needed to calculate the predicted future controls and outputs. This is of importance when constraints are to be applied based on the future predicted signals. The alternative method outlined, referred to as the vector-matrix solution, does not require this sequence of controllers to be found and it is very similar to the GPC form of solution. However, the LQG stability properties for the feedback loop are still retained