  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 paper, 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.
