  We show that Funnel MPC, a novel Model Predictive Control (MPC) scheme,
allows tracking of smooth reference signals with prescribed performance for
nonlinear multi-input multi-output systems of relative degree one with stable
internal dynamics. The optimal control problem solved in each iteration of
Funnel MPC resembles the basic idea of penalty methods used in optimization. To
this end, we present a new stage cost design to mimic the high-gain idea of
(adaptive) funnel control. We rigorously show initial and recursive feasibility
of Funnel MPC without imposing terminal conditions or other requirements like a
sufficiently long prediction horizon.
