Efficient implementation of multivariable MPC with parametric uncertainties

A robust predictive controller for uncertain multivariable systems is developed in this work. The design problem is based on multivariable Controlled Auto Regressive Integrated Moving Average (CARIMA) model with parametric uncertainties. The use of an uncertain CARIMA model leads to a non convex optimization problem. Consequently, the computation time is so high that limit the on line implementation of the robust predictive controller. To reduce the computation time, we propose, in this work, the convexification of the optimization problem by using the generalized geometric programming. This method is addressed for non convex polynomial problem which is the case of most robust and nonlinear control system analysis and design problem. The efficiency of the proposed optimization algorithm, LMI and genetic algorithms optimizers are tested and compared on benchmark functions. The proposed controller is performed on three tanks system.