具多比例时滞的双向联想记忆忆阻神经网络的无源性  

Passivity of Memristive Bidirectional Associative Memory Neural Networks with Multi-proportional Delays

作　　者：王芬 WANG Fen(School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521)

机构地区：[1]广东金融学院金融数学与统计学院,广州510521

出　　处：《工程数学学报》2024年第6期1053-1073,共21页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61907010);广东省教育厅普通高校重点领域专项(2020ZDZX3051).

摘　　要：在Filippov解的框架下,通过构造合适的Lyapunov-Krasovskii泛函,利用不等式性质、Schur补引理、集值映射理论和右侧不连续的泛函微分方程理论研究了具有多比例时滞的双向联想记忆(Bidirectional Associative Memory,BAM)忆阻神经网络的无源性问题。针对系统的多比例时滞项,采用非线性变换对其进行了变形处理,成功地建立了具有多比例时滞的BAM忆阻神经网络无源性的充分条件。这些条件不仅揭示了系统参数与无源性之间的关系,还为设计稳定、可靠且具有良好无源性的BAM忆阻神经网络提供了理论依据和指导。最后,通过两个例子验证了基于线性矩阵不等式结论的有效性。不仅深化了对BAM忆阻神经网络动态行为的理解,还为该类型网络在实际应用中的设计和优化提供了新的视角。Under the framework of Filippov solutions,passivity analysis of memristive BAM neural networks with multi-proportional delays can be guaranteed by constructing suitable Lyapunov-Krasovskii functional,Jensen’s inequality,Lemma of Schur Complement,the theory of set-valued maps and functional differential equations with discontinuous right-hand sides.Moreover,the terms of multi-proportional delays are deformed by nonlinear transformation in this paper.We have successfully established sufficient conditions for the passivity of BAM memristive neural networks with multiple proportional delays.These conditions not only reveal the relationship between system parameters and passivity,but also provide theoretical basis and guidance for designing stable,reliable,and well passive BAM memristive neural networks.Finally,two numerical examples are exploited to show the effectiveness of the derived LMI-based passivity conditions.The work presented in this article not only deepens the understanding of the dynamic behavior of BAM memristive neural networks,but also provides a new perspective for the design and optimization of this type of network in practical applications.

关 键 词：无源性 多比例时滞 神经网络 忆阻器 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]