Robust predictive control using tight sets of predicted states

A novel predictive controller for constrained linear time-varying systems w ith polytopic uncertainty is presented. The algorithm minimises an upper bo und on the predicted quadratic cost function with respect to the first few future control moves and a feedback gain that completes the description of the predicted input trajectory. The optimisation problem is shown to be a c onvex problem which can be formulated as a linear-matrix-inequality (LMI) p roblem. Constraints are handled by posing necessary and sufficient conditio ns on the first few future control moves and a sufficient condition on the moves thereafter; these conditions are formulated in terms of additional LM Is. The algorithm is shown to be asymptotically stable. An example illustra tes the efficiency of the method.