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类型 应用研究 预答辩日期 2017-11-20
开始(开题)日期 2016-06-07 论文结束日期 2017-09-13
地点 东南大学数学学院第一报告厅 论文选题来源 国家自然科学基金项目     论文字数 8 (万字)
题目 基于忆阻的神经网络的动力学分析及应用
主题词 忆阻,神经网络,动力学分析,高速路网
摘要 自2008年惠普公司的研究人员首次成功研制出基于TiO$_2$的忆阻器物理器件以后,人们掀起了 对忆阻器以及忆阻器神经网络的研究热潮。特别的,依靠超大规模集成电路构造出的忆阻神经网络 逐渐成为人们研究的焦点。此外,由于忆阻器本身的高存储量、小体积以及非易失性使其 展现出其广泛的应用前景。本文考虑了基于忆阻的神经网络的动力学行为,并讨论了它在交通路网中的应用。 全文共七章,第二章讨论具有概率时变延时的忆阻网络模型的无源性行为。第三章考虑了 忆阻神经网络的准同步和同步控制问题。 第四章研究了忆阻神经网络的有限时间和固定时间镇定问题。第五章 分析了忆阻神经网络的状态估计问题。第六章为离散时间神经网络的稳定性以及高速路网的全局鲁棒指数稳定性 问题。具体工作如下: 第二章研究了具有概率时变延时的忆阻网络模型的无源性行为, 在合理的假设条件下,借助Lyapunov函数和线性矩阵不等式技巧给出了保证忆阻网络无源的 充分性条件。 其中,考虑到网络的每个权重都在两个不同的常量值之间转换,因此,我们将 网络系数所有有可能的形式的组合个数$2^{2n^2}$依次排列。这种处理方式充分考虑了 忆阻网络的切换特性,使得本文所得结果更具 一般性,此外,这些判据中包含更多的参变量,这也显示出了文章所得结论的灵活性和优越性。 第三章考虑了忆阻神经网络的准同步和同步控制问题。首次,通过设计恰当的控制策略,在 矩阵测度的基础上,给出了保证目标神经网络准同步的代数判据。 其次,研究了忆阻神经网络的同步控制问题,基于不连续的控制法则, 并构造适当的Lyapunov函数,以线性矩阵不等式的形式得出了驱动-响应系统 同步的充分性判据。值得注意的是,与第二章结论不同,我们采用鲁棒分析方法 来处理所给出的忆阻网络模型,也即,通过可测函数的选取,将目标网络转化为 具有不确定参数的鲁棒系统,进而通过鲁棒分析技巧来相应的研究忆阻网络的 相关动力学行为,这种方法也为忆阻神经网络的处理带来的新的突破。 第四章通过Lyapunov函数方法以及不连续的控制技巧, 探讨了忆阻神经网络的有限时间和固定时间镇定问题。值得注意的是,有限时间的镇 定性结论依赖于状态的初始时刻,而固定时间镇定的结论则与系统的初始时刻无关,因此,为了 更好的区分和比较这两种镇定问题,也为了更好的提高所得结论的实用性,我们将以代数不等式的形式 给出保证系统镇定的判据。此外,为了使设计的控制器能够更快的得到响应, 我们可以通过简单 的计算得出系统达到稳定状态所需要的校正时间的上界。 第五章分析了忆阻神经网络的状态估计问题。通过采用李雅普诺夫函数、矩阵分析技术以及 设计恰当的非脆弱状态估计器,给出了保证估计误 差系统渐近稳定的充分条件。值得注意的是,首先 研究连续时间的网络模型的状态估计问题,进而将其推广至离散时间的情形。因此,本 章的结果可看做是对现有结论的延拓。 第六章研究了离散时间神经网络的稳定性及其在高速路网上的应用。 首先探讨了一类带有不确定参数的离散时间的神经网络的稳定性问题, 然后将所得结论运用到一类特殊的不确定离散网络,即高速路网中,利用高速路网每个 元胞之间车流量的递推关系以及高速路网平衡点的定义,讨论高速路网不拥堵平衡点 的鲁棒指数稳定性问题。这些判据 深刻揭示了离散时间的神经网络以及高速路网稳定性的动力学机理。
英文题目 Dynamics Analysis of Memristive Neural Networks and Its Applications
英文主题词 Memristor, Neural networks, Dynamic analysis, Freeway traffic system
英文摘要 The researches about memristor and memristor-based neural networks have generated world wide interest since the successful development of TiO$_2$-based memristor device by researchers of Hewlett-Packard company in 2008, especially for the memristive neural networks that build on the basis of VLSI circuit. In addition, considering its high storage, small size and non-volatile properties, which has shown wide applications. This paper considers the dynamic behaviors of memrisitve neural networks and then discusses its application in traffic networks. The paper is divided into seven main chapters. The second chapter discusses the passive analysis of memrisitve neural network with probability time-varying delays. The third chapter considers the quasi-synchronization and synchronization control of memristive neural networks. In the fourth chapter, the finite-time and fixed-time stabilization control of memristive neural networks are studied. The fifth chapter analysis the state estimation of the memristor-based neural networks. The sixth chapter is the global robust exponential stability analysis of the discrete time neural network as well as the highway traffic system. The detaild conclusions are as follows: The second chapter studies the passivity analysis of memristive neural networks with probabilistic time-varying delays, by means of some reasonable hypothesis, the Lyapunov function as well as linear matrix inequality (LMI) techniques, the corresponding sufficient conditions that ensure the memristive neural network is passive is given. In which, considering the network of each weights are switching between two different constant values, therefore, the combination number of the possible form of the connection weight is $2^{2n^2}$. This approach fully consider the characteristics of each connection weights, which makes the conclusions derived in this chapter is more general. In addition, the derived criteria contain more variables, which have more flexibility and superiority. The third chapter considers the quasi-synchronization and synchronization control of memristive neural network. First, by means of a proper control strategy as well as the matrix measure method. The algebraic criterion to ensure the quasi-synchronization of the target model is given. Then, on the basis of the discontinuous control law, and a suitable Lyapunov function, sufficient conditions are presented to guarantee the drive-response system reach synchronization goal. What is different from the second chapter is that the robust analysis method is employed to tackle with the target model, i.e., by introducing some measurable functions, the target model can be seen as a robust systems with uncertain parameters, and the this techniques can be used to deal with the corresponding dynamic behavior of the memristive neural networks, which also bring the new breakthrough to this kinds of system. In the fourth chapter, by means of the Lyapunov function method and the discontinuous control technique, the corresponding finite-time and fixed-time stabilization control strategy for delayed memristive neural networks were provided. It is worth noting that, the settling time of the finite-time stabilization heavily limited by the initial conditions of a system, which may constraint its widespread application, to overcome this shortcomings and make comparison with the fixed-time stabilization control method, the corresponding fixed-time stabilization criterion will be presented in the form of algebraic inequalities. Moreover, to guarantee a fast response, it is often reacquire the trajectories of the network states converge to some equilibrium point during a time interval, thus the upper bound of the settling time for stabilization is estimated. The fifth chapter analysis the state estimation of the memristive neural networks. By endowing the Lyapunov function, matrix analysis technique and a proper non-fragile state estimator, sufficient criteria for the stability findings are furnished. It is worth noting that, the state estimation of the continuous time system is first studied and then extended the derived conclusions to the discrete time case, which makes the results of this chapter be a continuation of the existing conclusions. The six chapter consider the sufficient conditions for the global robust exponential stability of the uncertain discrete-time system, and then the derived criterion is extended to freeway traffic system, which can be seen as a special case of uncertain discrete-time system. In the freeway traffic system, via the traffic flow of each cells and the definition of the uncongested equilibrium point, the corresponding conclusions are also reached, which can ensure the freeway system operating at an uncongested equilibrium state, achieving the goal of global robust exponential stability. These criteria are deeply reveal the dynamical mechanism of the discrete time neural networks as well as the freeway traffic systems.
学术讨论
主办单位时间地点报告人报告主题
复杂系统与网络科学研究中心 2016.4.12 东南大学数学学院第二报告厅 李若霞 Impulsive Effects and Stability Analysis on Memristive
复杂系统与网络科学研究中心 2016.5.10 东南大学数学学院第二报告厅 李若霞 Complete stability of feedback CNNs
复杂系统与网络科学研究中心 2016.11.8 东南大学数学学院第二报告厅 李若霞 Multiple Concentric Gating Traffic Control
复杂系统与网络科学研究中心 2016.12.8 东南大学数学学院第二报告厅 李若霞 Global exponential stabilization of freeway models
复杂系统与网络科学研究中心 2016.12.22 东南大学数学学院第二报告厅 李若霞 Global Exponential Stability for Discrete-Time
复杂系统与网络科学研究中心 2015.11.16 东南大学数学学院第二报告厅 李若霞 Memristor Overview up to 2015
复杂系统与网络科学研究中心 2016.3.15 东南大学数学学院第二报告厅 李若霞 Global Asymptotic Stability and Stabilization of
复杂系统与网络科学研究中心 2017.3.2 东南大学数学学院第二报告厅 李若霞 Robust global adaptive exponential stabilization of discrete-time systems
     
学术会议
会议名称时间地点本人报告本人报告题目
IEEE World Congress on Computational Intelligence 2016.7.24-2016.7.29 温哥华 加拿大 Finite-Time Stability Analysis of Fractional Order Delayed Memristive Neural Networks
第36届中国控制会议 2017.7.26-2017.7.28 辽宁 大连 State estimation for delayed neural networks
第29届中国控制与决策学术会议 2017.5.28-2017.5.30 重庆 Fixed-time stabilization control of reaction-diffusion Cohen-Grossberg
     
代表作
论文名称
Dissipativity analysis of memristive neural networks with time-varying delays and randomly occurring
Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying dela
Passivity analysis of memristive neural networks with probabilistic time-varying delays
Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen-
Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincare
Fixed-time synchronization of delayed memristor-based recurrent neural networks
Non-fragile state observation for delayed memristive neural networks: Continuous-time case and discr
Synchronization of delayed Markovian jump memristive neural networks with reaction-diffusion terms v
Adaptive projective synchronization of memristive neural networks with time-varying delays and stoch
Exponential and fixed-time synchronization of Cohen-Grossberg neural networks with time-varying dela
Finite-time stability analysis of fractional order delayed memristive neural networks
Fixed-time stabilization control of reaction-diffusion Cohen-Grossberg neural networks
 
答辩委员会组成信息
姓名职称导师类别工作单位是否主席备注
刘庆山 正高 教授 博导 华中科技大学 自动化学院
肖敏 正高 教授 博导 南京邮电大学 自动化学院
梁金玲 正高 教授 博导 东南大学 数学学院
林文松 正高 教授 博导 东南大学 数学学院
王冠军 正高 教授 博导 东南大学 数学学院
      
答辩秘书信息
姓名职称工作单位备注
聂小兵 副高 副教授 东南大学 数学学院