一类离散时间线性系统有限时间H_∞预测控制

Finite-time H_∞ Predictive Control for a Class of Linear Discrete-time System

针对一类时不变、有限能量外部干扰的线性离散时间系统,研究了有限时间H_∞预测控制问题.给出了线性系统有限时间H_∞预测控制问题的定义,通过构造Lyapunov-Krasovskii函数并结合矩阵不等式技术,给出了系统有限时间H_∞预测控制器有解的充分条件;进一步,将该问题转化为具有线性矩阵不等式约束的优化问题,并给出了相应的求解算法.数值算例和仿真对比表明了该设计方法的有效性.

The finite time H∞ predictive control problem for a class of linear discrete-time system with time-invarying finite-energy exogenous disturbance was discussed. The definition of finite time H∞ predictive control of linear system was given. Then by constructing Lyapunov-Krasovskii function and using linear matrix inequality approach, a sufficient condition for finite time H∞ predictive control of linear system was presented. Further- more,the problem is reduced to the optimization problem under the constraint of linear matrix inequalities and the corresponding solving algorithm was given. A numerical example and contrastive simulations show the effectiveness of the proposed method.