Robust Tube-Based Tracking MPC for Linear Systems with Multiplicative Uncertainty

Tracking of piece-wise constant references under multiplicative plant uncertainty is more difficult than regulating to the origin as a steady state is not known or does not exist. Therefore, current robust model predictive control algorithms consider the steady state as an additive disturbance, especially in case of varying references. This work uses a nominal steady state as a parameter for the terminal set and as an optimization variable which yields an increased feasible region. In addition, it is shown that such a terminal set can be computed in a finite number of iterations. The state evolution over the prediction horizon is bounded by polytopic tubes and the MPC algorithm is formulated as a quadratic problem. Moreover, offset-free tracking can be achieved when the nominal plant matches the true plant. A numerical example is given to show the effectiveness of the proposed method for short prediction horizons and changing references.