离散系统有限时间稳定预测控制

Finite Time Stable Predictive Control for Discrete Systems

摘要: 针对一类离散时间线性时不变系统，研究其有限时间稳定预测控制问题。将有限时间稳定的概念引入预测控制中，借助状态反馈，建立有限时间稳定与预测控制之间的联系。通过构造Lyapunov函数将有限时域的最小化优化问题转化为具有线性矩阵不等式的约束问题，采用线性矩阵不等式的方法，给出状态反馈控制率存在的充分条件。数值仿真结果验证了所提出方法的有效性。

Abstract: The finite-time stable predictive control problem for a class of discrete-time linear time-invariant systems is studied. The concept of finite-time stability is introduced into predictive control, and the relationship between finite-time stability and predictive control is established by the state feedback. The minimization optimization problem in finite time domain is transformed into a constrained problem with linear matrix inequalities by constructing the Lyapunov function. The sufficient conditions for the existence of state feedback control rate are given by using linear matrix inequalities. The numerical simulation results show the effectiveness of the proposed method.