Global Mittag–Leffler Stabilization of Fractional-Order Memristive Neural Networks
Global Mittag–Leffler Stabilization of Fractional-Order Memristive Neural Networks
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DOI：
10.1109/tnnls.2015.2506738
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发表时间：
2017
影响因子：
10.4
通讯作者：
Ailong Wu;Z. Zeng
中科院分区：
文献类型：
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作者：
Ailong Wu;Z. Zeng
根据传统的忆阻神经网络理论，神经动力学特性是解决类脑联想学习、动态信息存储或检索等领域许多问题的有力工具。然而，正如大多数分数阶系统中经常指出的那样，整数阶系统的系统分析方法不能直接扩展并应用于处理分数阶系统，因此，它在分析和控制分数阶忆阻神经网络中提出了困难的问题。利用集值映射和分数阶微分包含，结合一个新提出的分数阶微分不等式，研究了一类分数阶忆阻神经网络的全局Mittag-Leffler镇定问题.两种类型的控制规则（即，状态反馈镇定控制和输出反馈镇定控制）设计了分数阶忆阻神经网络的镇定方法，并建立了镇定准则列表.最后，通过两个数值算例说明了所得理论结果的有效性和特点。
According to conventional memristive neural network theories, neurodynamic properties are powerful tools for solving many problems in the areas of brain-like associative learning, dynamic information storage or retrieval, etc. However, as have often been noted in most fractional-order systems, system analysis approaches for integral-order systems could not be directly extended and applied to deal with fractional-order systems, and consequently, it raises difficult issues in analyzing and controlling the fractional-order memristive neural networks. By using the set-valued maps and fractional-order differential inclusions, then aided by a newly proposed fractional derivative inequality, this paper investigates the global Mittag-Leffler stabilization for a class of fractional-order memristive neural networks. Two types of control rules (i.e., state feedback stabilizing control and output feedback stabilizing control) are designed for the stabilization of fractional-order memristive neural networks, while a list of stabilization criteria is established. Finally, two numerical examples are given to show the effectiveness and characteristics of the obtained theoretical results.