Analysis of iterative learning control for a class of fractional differential equations

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• 作者：Shengda Liu ; JinRong Wang ; Wei Wei
• 关键词：PD ; type iterative learning control ; Fractional differential equations ; Mittag–Leffler functions ; Initial error
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：17-31
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we discuss PD-type learning control law for linear differential equations of fractional order \(\alpha \in (1,2)\). We derive convergence results for open-loop and closed-loop iterative learning schemes with zero initial error and random but bounded initial error in the sense of \(\lambda \)-norm by utilizing properties of Mittag–Leffler functions. Numerical examples are presented to demonstrate the validity of the design methods.