Yang Chao, Liu Yicheng, Huang Lihong
Department of Mathematics and Computer Science, Changsha University, Changsha, Hunan 410002 China.
Department of Mathematics, National University of Defense Technology, Changsha, 410073 China.
Cogn Neurodyn. 2022 Dec;16(6):1471-1483. doi: 10.1007/s11571-021-09778-8. Epub 2022 Mar 17.
This brief presents the finite-time stabilization and fixed-time stabilization of multiple memristor-based neural networks (MMNNs) with nonlinear coupling. Under the retarded memristive theory, the generalized Lyapunov functional method, extended Filippov-framework and Laplacian matrix theory, we can realize both the finite-time stabilization and fixed-time stabilization problem of MMNNs by designing novel state-feedback controller and the corresponding adaptive controller with regulate parameters. Moreover, we assess the bounds of settling time for the both two kinds of stabilization respectively, and we deeply analyze the influence of initial desiring values and the linear growth condition of the controller on the system. Finally, the benefits of the proposed approach and the experimental analysis are demonstrated by numerical examples.
本文介绍了具有非线性耦合的多个基于忆阻器的神经网络（MMNNs）的有限时间稳定和固定时间稳定。在延迟忆阻理论、广义李雅普诺夫泛函方法、扩展菲利波夫框架和拉普拉斯矩阵理论的基础上，通过设计新颖的状态反馈控制器和具有调节参数的相应自适应控制器，我们可以实现MMNNs的有限时间稳定和固定时间稳定问题。此外，我们分别评估了两种稳定方式的调节时间界限，并深入分析了初始期望值和控制器的线性增长条件对系统的影响。最后，通过数值例子证明了所提方法的优点和实验分析。
