【作者】 陈悦；

【导师】 朱松；

【作者基本信息】 中国矿业大学 ， 运筹学与控制论， 2025， 博士

【摘要】 近几十年来,神经网络凭借其卓越的动力学特性,尤其在稳定性和同步性方面的优势,已广泛应用于联想记忆、信号处理、组合优化、模式识别和保密通信等多个关键领域.由于放大器响应速度的限制以及神经元之间固有的信号传递延迟,时滞现象在神经网络的实际应用中不可避免.时滞的存在可能引发系统的不稳定性、震荡甚至混沌行为,从而严重影响系统的整体性能.因此,研究时滞对神经网络稳定性和同步控制的影响,不仅具有重要的理论价值,也对实际应用具有深远的意义.本文通过构造合适的Lyapunov函数,并结合不等式技术,系统地研究了几类时滞神经网络的动力学行为.具体而言,分析了时滞对网络稳定性和同步性的影响,探讨了包括渐近稳定性、指数同步控制、有限时间稳定性以及有限时间同步控制等在内的多个重要问题.具体而言,本文的主要工作如下:1)通过构造不同的Lyapunov函数,并运用Banach不动点定理和比较原则,本文分析了具有广义分段常变元的神经网络的渐近稳定性,得到了确保系统解存在唯一以及平衡点全局渐近稳定的几组充分条件.2)在事件触发控制下,通过构造不同的Lyapunov函数和参考系统,本文研究了多个时滞神经网络的同步性,给出了确保所考虑的多个时滞神经网络指数同步的若干代数条件.3)基于四元数的一些代数性质,本文考虑了驱动-响应四元值模糊忆阻神经网络的同步问题,分别在静态和动态事件触发条件下,给出使响应神经网络同步于驱动神经网络的若干代数准则.4)利用广义的Halanay不等式和现有的有限时间稳定性定理,本文讨论了具有有界时变时滞神经网络的有限时间同步问题,提出了一种改进的两步控制方法,实现了所考虑的驱动-响应时滞神经网络之间的有限时间同步.5)在有界时滞或无界时滞情形下,本文探讨了一类递归神经网络的有限时间同步问题,以广义Halanay不等式的形式给出了两个新颖的有限时间稳定性引理,并基于所得引理,给出了确保所考虑的驱动-响应时滞神经网络之间有限时间同步的若干准则.本文所得结果,尤其是在时滞神经网络有限时间控制方面,将进一步丰富时滞神经网络的动力学理论,有望为神经网络的实际应用提供一定的理论支持.更多还原

【Abstract】 In recent decades,neural networks have been widely applied in key areas such as associative memory,signal processing,combinatorial optimization,pattern recogni-tion,and secure communication,thanks to their outstanding dynamic characteristics,especially in terms of stability and synchronization.Due to the limitations of amplifi-er response speed and the inherent signal transmission delays between neurons,delay phenomena are inevitable in the practical application of neural networks.The presence of delays can lead to instability,oscillations,and even chaotic behavior in the system,severely affecting its overall performance.Therefore,studying the impact of delays on the stability and synchronization control of neural networks is of great theoretical im-portance and has profound significance for practical applications.This thesis systemat-ically investigates the dynamic behavior of several types of time-delay neural networks by constructing appropriate Lyapunov functions and applying inequality techniques.Specifically,it analyzes the effects of delays on the stability and synchronization of networks and explores multiple important issues,including asymptotic stability,ex-ponential synchronization control,finite-time stability,and finite-time synchronization control.Specifically,the main work of this thesis is as follows:1)By constructing different Lyapunov functions and applying the Banach fixed-point theorem and the comparison principle,this thesis analyzes the asymptotic stability of neural networks with generalized piecewise constant arguments.Several sufficient conditions are obtained to ensure the existence and uniqueness of the system’s solution and the global asymptotic stability of the equilibrium point.2)Under event triggered control,this thesis studies the synchronization of multiple time-delay neural networks by constructing different Lyapunov functions and reference systems,and provides several algebraic conditions to ensure exponential synchroniza-tion of the considered multiple time-delay neural networks.3)Based on some algebraic properties of quaternions,this thesis considers the syn-chronization problem of drive-response quaternion fuzzy memristive neural networks,and provides several algebraic criteria for synchronizing the drive neural network with the response neural network under static and dynamic event triggering conditions.4)Using the generalized Halanay inequality and existing finite-time stability the-orems,this thesis discusses the finite-time synchronization problem of neural networks with bounded time-varying delay and proposes an improved two-step control method to achieve finite-time synchronization between the considered drive-response delay neu-ral networks.5)This thesis explores the finite-time synchronization problem of a class of re-current neural networks under bounded or unbounded delays.Two novel finite-time stability lemmas are presented in the form of generalized Halanay inequalities,and based on the obtained lemmas,several criteria are given to ensure finite-time synchro-nization between the considered drive-response delayed neural networks.The results obtained in this thesis,especially in the finite-time control of time-delay neural networks,will further enrich the dynamic theory of time-delay neural networks and are expected to provide theoretical support for the practical application of neural networks.更多还原