Robust predictive control using tight sets of predicted states

A predictive controller for constrained linear time-varying systems with polytopic uncertainty is presented. The algorithm minimises an upper bound 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 convex problem which can be formulated as a linear-matrix-inequality (LMI) problem. Constraints are handled by posing necessary and sufficient conditions on the first few future control moves and a sufficient condition on the moves thereafter; these conditions are formulated in terms of additional LMIs. The algorithm is shown to be asymptotically stable. An example illustrates the efficiency of the method