It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real-world phenomena that occurs repeatedly. Singular systems are well-known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time-series analysis, and many other areas of science and technology. In this article, we investigate and analyze the convergence characteristic of PD-type iterative learning control (ILC) scheme for linear discrete-time singular system. We reformulate the discrete-time singular system as a kind of algebraic input-output transmission based on the lifted vector technique. The monotonic convergence has been deduced in the sense of 2-norm for the first-order as well as second-order PD-type ILC scheme. It is shown that the second-order PD-type ILC algorithm has good tracking performance than the first-order on the whole time interval. Finally, we perform comparative analysis to validate the results numerically.

中文翻译：

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离散时间奇异系统的PD型迭代学习控制分析

值得注意的是，迭代学习控制算法由于其对从现实世界中反复发生的现象发展而来的系统的跟踪控制的特殊性，具有很高的意义。奇异系统以其在网络分析、生物系统、经济系统、社会系统、工程系统、时间序列分析和许多其他科学技术领域的应用而闻名。在本文中，我们研究和分析了线性离散时间奇异系统的PD型迭代学习控制（ILC）方案的收敛特性。我们将离散时间奇异系统重新定义为一种基于提升向量技术的代数输入输出传输。对于一阶和二阶 PD 型 ILC 方案，已经在 2 范数的意义上推导出了单调收敛。结果表明，二阶 PD 型 ILC 算法在整个时间间隔上比一阶具有更好的跟踪性能。最后，我们进行比较分析，以数值验证结果。