STABILITY AND CONVERGENCE ANALYSES OF AN ADAPTIVE GPC BASED ON STATE-SPACE MODELING

A generalized predictive controller (GPC) is derived based on a genera l state-space model. The equivalence of the predictive control problem to a perturbation problem is revealed. In the case of a small perturb ation, the closed-loop poles are calculated with high accuracy. For th e case of a general perturbation, an upper bound on the permissible pe rturbation norm is derived assuming an open-loop stable system. Both t he plant-model match and plant-model mismatch cases are analysed. The controller is proven to be robust and an adaptive implementation is mo tivated. For open-loop stable systems, the convergence and stability o f the control scheme are ensured by proper tuning of the control weigh t and prediction horizon. The results are applicable to a wide range o f predictive controllers. The main contribution of this paper is not a new control algorithm, but new techniques to analyse the GPC as well as new stability and convergence results.