分数阶BAM模糊神经网络的全局Mittag-Leffler镇定  

Global Mittag-Leffler Stabilization of BAM Fuzzy Neural Networks with Fractional-Order

作　　者：李洁 陈胜龙 李洪利[1,2] 

机构地区：[1]新疆大学数学与系统科学学院,新疆 乌鲁木齐 [2]新疆应用数学重点实验室,新疆 乌鲁木齐

出　　处：《理论数学》2022年第11期1925-1933,共9页Pure Mathematics

摘　　要：本文解决了分数阶BAM模糊神经网络的全局Mittag-Leffler (M-L)镇定问题。首先回顾了与分数阶微积分相关的基础知识,并建立了网络模型。其次,基于一种新的压缩映射和二范数分析方法严格证明了模型平衡点的存在唯一性。最后,通过设计一种简洁有效的线性控制器导出了分数阶BAM模糊神经网络实现全局M-L镇定的充分性判据。This paper deals with the issue of global Mittag-Leffler (M-L) stabilization for fractional-order BAM fuzzy neural networks (FBAMFNNs). Firstly, some necessary knowledge related to fractional calculus are reviewed, and the model of FBAMFNN is established. Next, the existence and unique-ness of equilibrium point is proved based on constructing a novel contraction mapping and 2-norm analysis method. Finally, the sufficient criterion is derived to realize global M-L stabilization of FBAMFNNs by designing a concise and effective linear controller.

关 键 词：BAM神经网络 Mittag-Leffler镇定 分数阶 模糊逻辑 

分 类 号：O172[理学—数学] TP183[理学—基础数学]