On the design of Robust tube-based MPC for tracking ⋆

This paper deals with the design procedure of the recently presented robust MPC for tracking of constrained linear systems with additive disturbances. This controller is based on nominal predictions and it is capable to steer the nominal predicted trajectory to any target admissible steady state, that is retaining feasibility under any set point change. By means of the notion of tube of trajectories, robust stability and convergence is achieved. The controller formulation has some parameters which provides extra degrees of freedom to the design procedure of the predictive controller. These allow to deal with control objectives such as disturbance rejection, output offset prioritization or enlargement of the domain of attraction. In this paper, output prioritization method, LMI based design procedures and algorithms for the calculation of invariant sets are presented. The proposed enhanced design of the MPC is demonstrated by an illustrative example.