  Funnel MPC, a novel Model Predictive Control (MPC) scheme, allows guaranteed
output tracking of smooth reference signals with prescribed error bounds for
nonlinear multi-input multi-output systems. To this end, the stage cost
resembles the high-gain idea of funnel control. However, rigorous proofs for
initial and recursive feasibility without incorporating additional output
constraints in the Funnel MPC scheme are only available for systems with
relative degree one and stable internal dynamics. In this paper, we extend
these results to systems with relative degree two by incorporating also a term
based on the idea of a derivative funnel in the stage cost.
