Model predictive control of linear systems with nonlinear terminal control

In terminal weighting based model predictive control (MPC) algorithms, the terminal weighting term is used to cover the performance cost under the terminal control for guaranteeing stability. Therefore, the terminal control is crucial in choosing the terminal weighting term and also determining/estimating the stability region. However, most of the existing MPC algorithms are developed based on linear terminal control which restricts the achievable performance and stability of MPC. For linear systems, an MPC algorithm with nonlinear terminal control is presented in this paper, where the gain of the terminal control varies with the terminal state. An offline algorithm is proposed to determine the nonlinear gains and to choose the associated terminal weighting term. It is shown that, compared with the MPC algorithms with fixed linear terminal gain, a nonlinear terminal control results in a much larger stability region, which is confirmed by a numerical example.