正则系统在Lebesgue-p范数意义下的快速迭代学习控制

针对一类线性正则系统，传统迭代学习控制算法收敛速度较低的问题，设计了一种快速迭代学习控制算法。该算法在传统P型迭代学习控制算法基础上，增加了由相邻两次迭代时跟踪误差构成的上一次差分信号和当前差分信号，并在Lebesgue-p范数度量意义下，利用卷积推广的Young不等式严格证明了，当迭代次数趋于无穷大时，系统的跟踪误差收敛于零，并给出了算法的收敛条件。该算法与传统P型迭代学习控制算法相比，不仅提高了收敛速度，而且还避免了采用λ范数度量跟踪误差的缺陷，最后通过仿真结果进一步验证了所提算法的有效性。

Fast iterative learning control for regular system in sense of Lebesgue-p norm

Focused on the problem that the convergence speed of traditional iterative learning control algorithm used in linear regular systems is slow, a kind of fast iterative learning control algorithm was designed for a class of linear regular systems. Compared with the traditional P-type iterative learning control algorithm, the algorithm increases tracking error at neighboring two iterations generated from last difference signal and present difference signal. And the convergence of the algorithm was proven by using Yong inequality of convolutional inference in the sense of Lebesgue-p norm. The results show the tracking error of the system will converge to zero with infinite iterations. The convergence condition is also given. Compared with P-type iterative learning control, the proposed algorithm can fasten the convergence and avoid the shortcomings of using λ norm to measure the tracking error. Simulation further testifies the validity and effectiveness.