分数阶非线性系统PDα型迭代学习控制收敛性分析

兰州理工大学学报 ›› 2022, Vol. 48 ›› Issue (5): 92-98.

• 自动化技术与计算机技术 • 上一篇下一篇

分数阶非线性系统PD^α型迭代学习控制收敛性分析

张克军^*1,2, 彭国华², 杜永军³

1.徐州工程学院数学与统计学院, 江苏徐州 221018;
2.西北工业大学数学与统计学院, 陕西西安 710129;
3.兰州理工大学经济管理学院, 甘肃兰州 730050

收稿日期:2021-04-28 出版日期:2022-10-28 发布日期:2022-11-21
通讯作者: 张克军(1979-),男,山东临沂人,博士,副教授. Email:zhangkj2002@163.com
基金资助:
国家自然科学基金(12071408),江苏省自然科学基金(BK20201149),徐州市科技项目(KC18013)

Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems

ZHANG Ke-jun^1,2, PENG Guo-hua², DU Yong-jun³

1. School of Mathematics and Statistics, Xuzhou Institute of Technology, Xuzhou 221018, China;
2. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China;
3. School of Economics and Management, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2021-04-28 Online:2022-10-28 Published:2022-11-21

摘要/Abstract

摘要： 针对一类单输入单输出的分数阶非线性连续系统,利用卷积的推广Young不等式,分别研究了开环、闭环以及开闭环PD^α型分数阶迭代学习控制算法在L^p范数意义下收敛的充分条件,并进行了严格的理论证明.研究发现:控制算法收敛的充分条件取决于算法的增益和系统自身属性;在控制算法选取适当增益的情况下,开闭环PD^α型控制算法拥有比开环算法更快的收敛速度.这些结论与分数阶线性系统是相同的.仿真实验进一步验证了上述理论的可行性和正确性.

关键词: 分数阶, 迭代学习控制, L^p范数, 收敛性

Abstract: For a class of single input and single output (SISO) fractional-order nonlinear continuous systems, by taking advantage of the generalized Young inequality of convolution integral, the sufficient conditions for the convergence of open-loop, closed-loop and open-closed-loop PD^α type fractional-order iterative learning control (FOILC) algorithms are presented in the sense of L^p norm with strict theoretical proof of these algorithms followed. It is found that the sufficient conditions for the convergence of the control algorithms depend on the gains of the algorithms and the attributes of the systems themselves. The open-closed-loop PD^α-type control algorithm has faster convergence speed than the open-loop control algorithm under appropriate gain matrices. These conclusions are the same as those of fractional-order linear systems. The simulation experiments further verify the feasibility and the correctness of the above theory.

Key words: fractional-order, iterative learning control, L^p norm, convergence

中图分类号:

TP13

张克军, 彭国华, 杜永军. 分数阶非线性系统PD^α型迭代学习控制收敛性分析[J]. 兰州理工大学学报, 2022, 48(5): 92-98.

ZHANG Ke-jun, PENG Guo-hua, DU Yong-jun. Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems[J]. Journal of Lanzhou University of Technology, 2022, 48(5): 92-98.

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分数阶非线性系统PD^α型迭代学习控制收敛性分析

Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems

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分数阶非线性系统PDα型迭代学习控制收敛性分析

Convergence analysis of PDα type iterative learning control for a class of fractional-order nonlinear systems

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分数阶非线性系统PD^α型迭代学习控制收敛性分析

Convergence analysis of PD^α type iterative learning control for a class of fractional-order nonlinear systems