Abstract: For a class of linear singular systems, this paper studies on?the convergence characteristics of P-type iterative learning control in discrete frequency domain. Firstly, in the discrete frequency domain, the singular value?decomposition of the singular systems is carried out. Using the properties of Fourier series and the discrete frequency Parseval’s energy equality, the discrete energy spectrum recursive relation and character of the tracking errors are deduced. And the sufficient condition for monotone convergence of the first-order P-type iterative learning control law is obtained. Then, the convergence of the second-order learning law is discussed. The simulation experiment validates the correctness of the theory and the validity of this algorithm.

Key words: iterative learning control, linear singular systems, discrete frequency domain, Parseval’s energy equality

摘要： 针对一类线性广义系统，研究其P型迭代学习控制在离散频域中的收敛性态。在离散频域中，对广义系统进行奇异值分解后，利用傅里叶级数系数的性质和离散的Parseval能量等式，推演了一阶P型迭代学习控制律跟踪误差的离散能量频谱的递归关系和特性，获得了学习控制律收敛的充分条件；讨论了二阶P型迭代学习控制律的收敛条件。仿真实验验证了理论的正确性和学习律的有效性。

关键词: 迭代学习控制, 线性广义系统, 离散频域, Parseval能量等式