Constrained Robust Optimal Trajectory Tracking: Model Predictive Control Approaches

This thesis is concerned with the theoretical foundations of Robust Model Predictive Control and its application to tracking control problems. Its first part provides an introduction to MPC for constrained linear systems as well as a survey of different Robust MPC methodologies. The second part consists of a discussion of the recently developed Tube-Based Robust MPC framework and its extension to outputfeedback and tracking control problems. Guidelines on how to synthesize Tube-Based Robust Model Predictive Controllers are given, and a software framework is developed allowing for the controllers to be implemented both explicitly as a lookup table (using multiparametric programming) and implicitly by using fast on-line optimization algorithms. The reviewed Tube-Based Robust MPC controllers are tested on illustrative benchmark problems and issues concerning their computational complexity are discussed. The last part of this thesis presents the novel contribution of “Interpolated Tube MPC”, an approach that combines interpolation techniques with the basic ideas behind Tube-Based Robust MPC. Important properties of this new type of controller are proven in a rigorous theoretical analysis. Finally, the applicability of Interpolated Tube MPC is tested in a case study, which shows the superior computational performance of the controller compared to standard Tube-Based Robust MPC.