A stable model predictive control algorithm without terminal weighting

The introduction of terminal penalty in the performance index and the usage of the concept of terminal regions now become common practice in Model Predictive Control (MPC) for guaranteeing its stability. However, it is quite difficult and conservative to propagate the influence of disturbances and uncertainties from an initial state to the terminal state, in particular, when the predictive horizon is long. This paper presents a new stable MPC algorithm where the additional weighting on the first state rather than on the terminal state in the horizon is imposed. Furthermore, a new tuning knob is introduced in the performance index, which can be used to trade off between disturbance attenuation/robustness and stability. It is shown that in the absence of disturbances and uncertainties, the new MPC algorithm achieves the similar performance as current terminal weighting based MPC algorithms. However, it exhibits much better disturbance attenuation ability and robustness against uncertainties. The proposed method is favorably compared with terminal weighting based MPC algorithms by a numerical example.