具有时滞的分数阶忆阻神经网络固定时间同步

doi:10.16180/j.cnki.issn1007-7820.2023.08.012

摘要/Abstract

摘要：

文中研究了分数阶忆阻神经网络的固定时间同步问题。根据忆阻器的电压电流特性,建立一类具有时变时滞的分数阶忆阻神经网络模型。与传统的基于最大绝对值的记忆突触权值计算方法不同,通过引入数学变换,利用微分包含理论和集值映射,在Filippov解的框架下将分数阶忆阻神经网络转化为一类具有不确定参数的分数阶系统。在固定时间稳定性理论和可测选择定理的基础上,通过构造Lyapunov函数和利用不等式技术给出其固定时间同步的充分条件,并给出同步时间上界的计算式。通过反馈控制方法,构造合适的状态反馈控制器,使主从系统实现固定时间同步,且同步时间的上界与系统初始状态无关。通过仿真算例可看出所设计的控制器可以使系统快速地实现同步。

关键词: 忆阻神经网络, 分数阶微积分, 时变时滞, 反馈控制, 固定时间同步, Lyapunov稳定性理论, Filippov理论, 微分包含, 集值映射

Abstract:

The fixed-time synchronization problems are solved for fractional-order memristive neural networks. According to the voltage and current characteristics of memristors, the model of fractional-order memristive neural networks with time-varying delays is established. Different from the traditional calculation method of memristive synaptic weights based on the maximum absolute value, by introducing some transformations, using differential inclusion theory and set-valued maps, the fractional-order memristive neural networks are transformed into a type of fractional-order systems with uncertain parameters in the framework of Filippov solution. Based on the fixed-time stability theory and the theory of measurable selection, the sufficient conditions of fixed-time synchronization are given by constructing Lyapunov function and using inequality techniques, and the calculation formula of the upper bound for the synchronization time is given. By designing an appropriate state feedback controller, the master-slave systems can reach fixed-time synchronization, and the upper bound for the synchronization time is independent of the initial state for the systems. The simulation example shows that the designed controller makes the systems achieve synchronization quickly.

Key words: memristive neural networks, fractional-order calculus, time-varying delays, feedback control, fixed-time synchronization, Lyapunov stability theory, Filippov theory, differential inclusion, set-valued map

中图分类号:

TP13

王柯杰,童东兵. 具有时滞的分数阶忆阻神经网络固定时间同步[J]. 电子科技, 2023, 36(8): 81-87.

WANG Kejie,TONG Dongbing. Fixed-Time Synchronization for Fractional-Order Memristive Neural Networks with Time-Delays[J]. Electronic Science and Technology, 2023, 36(8): 81-87.

图/表 4

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