Stability of Soft-Constrained Finite Horizon Model Predictive Control

This paper addresses the stability of soft-constrained model predictive control (MPC). It is shown that the infinite horizon soft-constrained MPC problem can be solved as a finite horizon soft-constrained MPC problem if the prediction horizon is greater than an upper bound. The contribution of this paper is a procedure to compute the prediction horizon upper bound, which guarantees the stability. The proposed technique is verified using two simulation examples. The second example (inverted pendulum) is verified through practical implementation.