Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints

In this note, a new formulation of Model Predictive Control (MPC) framework with no stability-related terminal constraint is proposed and its stability is proved under mild standard assumptions. The novelty in the formulation lies in the use of timevarying monotonically increasing stage cost penalty. The main result is that the 0-reachability prediction horizon can always be made stabilizing provided that the increasing rate of the penalty is made sufficiently high.