Transient Performance of MPC for Tracking

We analyse the closed-loop performance of a model predictive control (MPC) for tracking formulation with artificial references. It has been shown that such a scheme guarantees closed-loop stability and recursive feasibility for any externally supplied reference, even if it is unreachable or time-varying. The basic idea is to consider an artificial reference as an additional decision variable and to formulate generalised terminal ingredients with respect to it. In addition, its offset is penalised in the MPC optimisation problem, leading to closed-loop convergence to the best reachable reference. In this letter, we provide a transient performance bound on the closed loop using MPC for tracking. We employ mild assumptions on the offset cost and scale it with the prediction horizon. In this case, an increasing horizon in MPC for tracking recovers the infinite horizon optimal solution.