Lebesgue-p范数意义下对初态误差进行加速修正的迭代学习控制

Accelerated modify approach for initial state error iterative learning control in sense of Lebesgue-p norm

针对一类多输入多输出线性时不变系统,提出一种初态误差加速修正的PD-型迭代学习算法.针对系统的任意初始状态,在时间轴上设计一个随迭代次数增加而缩短的修正区间.在该区间上,控制算法对初始状态偏差进行修正;修正区间外,算法与无初始误差的学习律等同.在Lebesgue-p范数度量跟踪误差意义下,利用卷积的推广Young不等式证明了所提出学习控制律的收敛性.数值仿真验证了该控制律的有效性.

This paper proposes a kind of proportional-derivative-type（PD-type） iterative learning control method of accelerated modifying the initial state error for a class of multi-input and multi-output linear time-invariant system. The special time intervals, which can effectively shrink with the increasing of the iterations number, is designed for the system with any initial states. In this interval, the initial state deviation is corrected by using some control algorithm, while in the outside of the interval, the algorithm is the same as the one for the system without the initial state error. When the error is tracked in the sense of Lebesgue-p norm, the monotone convergence of the presented learning control is proved by a generalized Young inequality. Numerical simulation results show the effectiveness of the control law.