Stability proof for nonlinear MPC design using monotonically increasing weighting profiles without terminal constraints
This work provides a theoretical stability guarantee for MPC designs that avoid terminal constraints, which is relevant for control practitioners seeking simpler implementations.
The paper proposes a new MPC formulation without terminal constraints, using time-varying monotonically increasing stage cost penalties, and proves stability under mild assumptions by showing that a sufficiently high penalty increase rate ensures stability.
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 time-varying 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.