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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.
Aiming at a class of multi-input and multi-output linear time-invariant systems, a PD-type iterative learning algorithm is proposed to accelerate the initial state error correction. For any initial state of the system, a correction is made on the time axis that shortens as the number of iterations increases The control algorithm is used to correct the initial state deviation, and the algorithm is the same as the learning law without initial error except for the correction interval.In the sense of Lebesgue-p norm metric tracking error, by using the Young’s inequality of convolution The convergence of the proposed control law is validated by numerical simulation.