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
DOI: 10.12677/PM.2022.1211207, PDF,    科研立项经费支持
作者: 李 洁, 陈胜龙：新疆大学数学与系统科学学院，新疆 乌鲁木齐；李洪利*：新疆大学数学与系统科学学院，新疆 乌鲁木齐；新疆应用数学重点实验室，新疆 乌鲁木齐
关键词: BAM神经网络；Mittag-Leffler镇定；分数阶；模糊逻辑；BAM Neural Networks； Mittag-Leffler Stabilization； Fractional-Order； Fuzzy Logic
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。
Abstract: 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.
文章引用：李洁, 陈胜龙, 李洪利. 分数阶BAM模糊神经网络的全局Mittag-Leffler镇定[J]. 理论数学, 2022, 12(11): 1925-1933. https://doi.org/10.12677/PM.2022.1211207

参考文献

[1] Chen, G., Zhou, J. and Liu, Z. (2004) Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models. International Journal of Bifurcation and Chaos, 14, 2229-2240. [Google Scholar] [CrossRef] 
[2] Wang, L., Dong, T. and Ge, M.-F. (2018) Finite-Time Syn-chronization of Memristor Chaotic Systems and Its Application in Image Encryption. Applied Mathematics and Com-putation, 347, 293-305. [Google Scholar] [CrossRef] 
[3] Kosko, B. (1987) Adaptive Bidirectional Associative Memories. Applied Optics, 26, 4947-4960. [Google Scholar] [CrossRef] 
[4] Cao, J. and Xiao, M. (2007) Stability and Hopf Bifurcation in a Sim-plified BAM Neural Networks with Two Delays. IEEE Transactions on Neural Networks, 18, 416-430. [Google Scholar] [CrossRef] 
[5] Mohamed Thoiyab, N., Muruganantham, P., Zhu, Q. and Gunasekaran, N. (2021) Novel Results on Global Stability Analysis for Multiple Time-Delayed BAM Neural Networks under Parameter Uncertainties. Chaos, Solitons & Fractals, 152, Article ID: 111441. [Google Scholar] [CrossRef] 
[6] Duan, L. and Li, J. (2021) Fixed-Time Synchronization of Fuzzy Neutral-Type BAM Memristive Inertial Neural Networks with Proportional Delays. Information Sciences, 576, 522-541. [Google Scholar] [CrossRef] 
[7] Yang, T. and Yang, L.-B. (1996) The Stability of Fuzzy Cellular Neural Networks. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 43, 880-883. [Google Scholar] [CrossRef] 
[8] Tang, Y., Yang, X., Wan, X., Zhou, Y., Cheng, Z. and Fardoun, H. (2019) Finite-Time Synchronization of Nonidentical BAM Discontinuous Fuzzy Neural Networks with Delays and Impulsive Effects via Non-Chattering Quantized Control. Communications in Nonlinear Science and Numerical Simulation, 78, Article ID: 104893. [Google Scholar] [CrossRef] 
[9] Li, H., Hu, C., Zhang, L., Jiang, H., and Cao, J. (2022) Complete and Finite-Time Synchronization of Fractional-Order Fuzzy Neural Networks via Nonlinear Feedback Control. Fuzzy Set and Systems, 443, 50-69. [Google Scholar] [CrossRef] 
[10] Chen, S., Li, H., Kao, Y., Zhang, L. and Hu, C. (2021) Finite-Time Stabilization of Fractional-Order Fuzzy Quaternion-Valued BAM Neural Networks via Direct Quaternion Approach. Journal of the Franklin Institute, 358, 7650-7673. [Google Scholar] [CrossRef] 
[11] Aouiti, C. and Jallouli, H. (2021) New Feedback Control Techniques of Quaternion Fuzzy Neural Networks with Time-Varying Delay. International Journal of Robust and Nonlinear Control, 31, 2783-2809. [Google Scholar] [CrossRef] 
[12] Zhang, T., Zhou, J. and Liao, Y. (2022) Exponentially Stable Periodic Os-cillation and Mittag-Leffler Stabilization for Fractional-Order Impulsive Control Neural Networks with Piecewise Caputo Derivatives. IEEE Transactions on Cybernetics, 52, 9670-9683. [Google Scholar] [CrossRef] 
[13] Klbas, A., Srivastava, H. and Trujillo, J. (2006) Theory and Application of Fractional Differential Equations. Elsevier, New York.
[14] Mitrinovic, D. and Vasic, P. (1970) Analytic Inequalities. Springer, Berlin.
[15] Yu, J., Hu, C., Jiang, H. and Fan, X. (2014) Projective Synchronization for Fractional Neural Networks. Neural Networks, 49, 87-95. [Google Scholar] [CrossRef] [PubMed]
[16] Li, H., Hu, C., Jiang, Y., Zhang, L. and Teng, Z. (2016) Global Mittag-Leffler Stability for a Coupled System of Fraction-al-Order Differential Equations on Network with Feedback Controls. Neurocomputing, 214, 233-241. [Google Scholar] [CrossRef] 

为你推荐