An Overview of Dynamics Analysis and Control of Memristive Neural Networks With Delays
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摘要: 忆阻器(Memristor)是一种无源的二端电子元件, 同时也是一种纳米级元件, 具有低能耗、高存储、小体积和非易失性等特点. 作为一种新型的存储器件, 忆阻器的研制, 有望使计算机实现人脑特有的信息存储与信息处理一体化的功能, 打破目前冯·诺伊曼(Von Neumann)计算机架构, 为下一代计算机的研制提供一种全新的架构. 鉴于忆阻器与生物神经元突触具有十分相似的功能, 使忆阻器得以充当人工神经元的突触, 建立起一种基于忆阻器的人工神经网络即忆阻神经网络. 忆阻器的问世, 为人工神经网络从电路上模拟人脑提供了可能, 必将极大推动人工智能的发展. 此外, 忆阻神经网络的硬件实现及信号传递过程中, 不可避免会出现时滞与分岔等现象, 因此讨论含各种时滞, 如离散、分布、泄漏时滞以及它们混合的时滞忆阻神经网络系统更具有现实意义. 首先介绍了忆阻器的多种数学模型及其分类, 建立了时滞忆阻神经网络(Delayed memristive neural networks, DMNN)的数学模型并阐述了其优点. 然后提出了处理时滞忆阻神经网络动力学行为与控制问题的两种思路, 详细综述了时滞忆阻神经网络系统的稳定性(镇定)、耗散性与无源性及其同步控制方面的内容, 简述了其他方面的动力学行为与控制, 并介绍了时滞忆阻神经网络动力学行为与控制研究新方向. 最后, 对所述问题进行了总结与展望.Abstract: A memristor is a passive two-terminal electronic element and is also a nanometer element. Meanwhile, it has the features of low-energy consumption, high-storage, small-volume and non-volatility. As a new type of memory device, the memristor has similar characteristics as human brain synapses, which is expected to realize the integration of information storage and processing and breaks through the bottleneck of the current Von Neumann computer architecture, and provides new design architecture for the next generation of computer. Since the distinct characteristic is its memory function, which is very similar to the synapse of biological neurons. In recent years, some researchers have replaced the synaptic connections in neural networks by the memristor, and have established a type of neural networks based on the memristor. In a word, the advent of the memristor makes it possible for artificial neural networks to simulate the human brain, greatly promoting the development of artificial intelligence. In addition, time delays are inevitable in hardware implementations and signal transmission of the memristive neural networks. It is thus crucial to discuss the memristive neural networks with discrete, distributed, leakage and mixed delays. Firstly, this paper introduces numerous kinds of the memristor mathematic models and its classification. We model the delayed memristive neural networks (DMNN) and point out their advantages. Secondly, two ways to deal with the dynamical behaviors and control of the DMNN are provided. The stability (stabilization), passivity and dissipativity, synchronization for the DMNN are elaborated while other dynamical behaviors and control are sketched. New research directions of dynamical behaviors and control of the DMNN are also presented. Finally, a summary and outlook is given.
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Key words:
- Memristor /
- time-varying delay /
- memristive neural networks /
- dynamical behaviors /
- control
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表 1 四类忆阻器
Table 1 Four classes of memristors
种类 电流控制型 电压控制型 理想型忆阻器 $v = M(q)i$ $i = W(\varphi )v$ $\dfrac{ {{\rm{d}}q} }{ {{\rm{d}}t} } = i$ $\dfrac{ {{\rm{d}}\varphi } }{ {{\rm{d}}t} } = v$ 理想通用型忆阻器 $v = M(x)i$ $i = W(x)v$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = f(x)i$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = g(x)v$ 通用型忆阻器 $v = M(x)i$ $i = W(x)v$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = f(x,i)$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = g(x,v)$ 拓展型忆阻器 $\begin{align} v = M(x,i)i \\ M(x,0) \ne \infty \end{align}$ $\begin{align} i = W(x,v)v \\ W(x,v) \ne 0 \end{align}$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = f(x,i)$ $\dfrac{ {{\rm{d}}x} }{ {{\rm{d}}t} } = g(x,v)$ 
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