Stability and convergence analysis of an adaptive GPC based on state space modeling

A generalized predictive controller (GPC) is derived based on a general state-space model. The link between the predictive control problem and the perturbation problem is highlighted. In the case of small perturbation, the closed-loop poles are calculated with high accuracy. For the case of a general perturbation, an upper bound on the permissible perturbation norm is derived assuming an open-loop stable system. Both the plant-model match and plant-model mismatch cases are analyzed. The controller is so robust that an adaptive implementation is motivated. For open-loop stable systems,the convergence and stability of the control scheme are insured by proper tuning of the control weight and prediction horizon. The results are applicable to a wide range of predictive controllers