An ellipsoidal off-line robust model predictive control strategy for uncertain polytopic discrete-time systems

Abstract

In this paper, an off-line robust model predictive control strategy for uncertain polytopic discrete-time systems is presented. The on-line computational burdens are reduced by precomputing off-line the sequence of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids. The real-time state feedback gain is then calculated by solving a numerically low-demanding optimization problem. The nominal model of the plant is included in the controller design in order to improve control performance. An overall algorithm is proved to guarantee robust stability.