非线性预测控制终端约束集的优化

In order to guarantee stability in model predictive control, one classic strategy is to add in the involved model predictive control optimization problem a terminal set and a terminal penalty, where the terminal set is an invariant set with the so-called terminal control law, and the terminal penalty is a local control Lyapunov function of the considered systems. In this paper, a novel scheme is proposed to obtain the terminal set, terminal control law and terminal penalty of nonlinear systems. Extra degrees are added to reduce the conservativeness of the offline optimization problem. Thus, it can guarantee theoretically the obtained terminal set is large. Since a large terminal set in principle implies a small prediction horizon in the online optimization problem, it can reduce the online computational burden accordingly. The extra degrees decouple the terminal set and terminal penalty to some extent, i.e., differently with the existing method, the terminal set is no longer a sub-level set of the terminal penalty anymore. A simulation example shows the effectiveness of the proposed scheme.