Robustness of globally exponential stability of delayed neural networks in the presence of random disturbances

This paper analyzes the robustness of globally exponential stability of time-varying delayed neural networks (NNs) subjected to random disturbances. Given a globally exponentially stable neural network, and in the presence of noise, we quantify how much noise intensity that the delayed neural network can remain to be globally exponentially stable. We characterize the upper bounds of the noise intensity for the delayed NNs to sustain globally exponential stability. The upper bounds of parameter uncertainty intensity are characterized by using transcendental equation. A numerical example is provided to illustrate the theoretical result.     

Robustness analysis of global exponential stability of neural networks with Markovian switching in the presence of time-varying delays or noises

In this paper, we analyze the robustness of global exponential stability of neural networks with Markovian switching (NNwMS) subject to random disturbances or time-varying delays. Given a globally exponentially stable neural network with Markovian switching, the problems to be addressed herein are how much noises or time delays that the neural networks can remain to be globally exponentially stable. We characterize the upper bounds of the time delays or noise intensity for the NNwMS to sustain global exponential stability. Two numerical examples are provided to illustrate the theoretical results.     

离散Hopfield双向联想记忆神经网络的稳定性分析

首先将离散Hopfield双向联想记忆神经网络转化成一个特殊的离散Hopfield网络 模型.在此基础上,对离散Hopfield双向联想记忆神经网络的全局渐近稳定性和全局指数稳 定性进行了新的分析.证明了神经网络连接权矩阵在给定的约束条件下有唯一的而且是渐近 稳定的平衡点.利用Lyapunov方程正对角解的存在性得到了几个判定平衡点为全局渐近稳 定和全局指数稳定的充分条件.这些条件可以用于设计全局渐近稳定和全局指数稳定的神经 网络.所做的分析扩展了以前的稳定性结果.     

Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks

This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme.      

A general projection neural network for solving monotone variational inequalities and related optimization problems

Recently, a projection neural network for solving monotone variational inequalities and constrained optimization problems was developed. In this paper, we propose a general projection neural network for solving a wider class of variational inequalities and related optimization problems. In addition to its simple structure and low complexity, the proposed neural network includes existing neural networks for optimization, such as the projection neural network, the primal-dual neural network, and the dual neural network, as special cases. Under various mild conditions, the proposed general projection neural network is shown to be globally convergent, globally asymptotically stable, and globally exponentially stable. Furthermore, several improved stability criteria on two special cases of the general projection neural network are obtained under weaker conditions. Simulation results demonstrate the effectiveness and characteristics of the proposed neural network.     

Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain

This paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity, while the delay accounts for the finite switching speed of the neuron amplifiers, or the finite signal propagation speed. It is known that the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability. The goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay. More precisely, conditions are given under which there is a unique equilibrium point of the neural network, which is globally exponentially stable for the states, with a known convergence rate. The conditions are easily testable and independent of the delay. Moreover, global convergence in finite time of the state and output is investigated. In doing so, new interesting dynamical phenomena are highlighted with respect to the case without delay, which make the study of convergence in finite time significantly more difficult. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations but without delays.     

输入向量控制细胞神经网络全局指数稳定

利用输入向量来控制细胞神经网络的稳定性.所得结果表明,当输入向量的绝对值大于某个仅仅只与细胞神经网络的物理参数有关的值时,不附加其它任何条件,细胞神经网络是全局指数稳定的.也讨论了输入向量的部分分量的绝对值大于某个仅仅只与细胞神经网络的物理参数有关的值时,细胞神经网络的全局指数稳定性,所得结论推广和改进了某些已有文献的相应结果.     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin’s continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained.     

Structural stability of unsupervised learning in feedback neuralnetworks

Structural stability is proved for a large class of unsupervised nonlinear feedback neural networks, adaptive bidirectional associative memory (ABAM) models. The approach extends the ABAM models to the random-process domain as systems of stochastic differential equations and appends scaled Brownian diffusions. It is also proved that this much larger family of models, random ABAM (RABAM) models, is globally stable. Intuitively, RABAM equilibria equal ABAM equilibria that vibrate randomly. The ABAM family includes many unsupervised feedback and feedforward neural models. All RABAM models permit Brownian annealing. The RABAM noise suppression theorem characterizes RABAM system vibration. The mean-squared activation and synaptic velocities decrease exponentially to their lower hounds, the respective temperature-scaled noise variances. The many neuronal and synaptic parameters missing from such neural network models are included, but as net random unmodeled effects. They do not affect the structure of real-time global computations     

具有时滞的双向联想记忆神经网络的定性分析

文中通过经入一个关键性条件研究了具有时滞的双向联想记忆神经的定性性质。这一关键性条件关联了网络双向的联结权系数。在这一条件下,证明了网络存在唯一的平衡态,并且这一平衡态是全局指数稳定的。当网络的外部输入具有周期性时,利用上述条件证明了网络存在全局平稳振荡。     

Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks

We show that an n-neuron cellular neural network with time-varying delay can have 2(n) periodic orbits located in saturation regions and these periodic orbits are locally exponentially attractive. In addition, we give some conditions for ascertaining periodic orbits to be locally or globally exponentially attractive and allow them to locate in any designated region. As a special case of exponential periodicity, exponential stability of delayed cellular neural networks is also characterized. These conditions improve and extend the existing results in the literature. To illustrate and compare the results, simulation results are discussed in three numerical examples.     

Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network     

小波网络在带噪声的混沌时间序列预测中的研究

在采用网络模型对带有噪声的混沌时间序列进行建模的过程中,噪声会影响模型的泛化能力。针对上述问题,本文提出了基于小波去噪的小波网络预测框架。在预处理阶段使用小波阈值方法抑制噪声,运用相空间重构理论确定嵌入维数和延迟时间,进而确定改进的小波网络模型的结构,结合BP算法和遗传算法对模型的参数进行学习。最后,在带噪声的Mackey-Glass混沌序列预测实验中验证了该框架的有效性。     

Delay-dependent state estimation for delayed neural networks

In this letter, the delay-dependent state estimation problem for neural networks with time-varying delay is investigated. A delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. The proposed method is based on the free-weighting matrix approach and is applicable to the case that the derivative of a time-varying delay takes any value. An algorithm is presented to compute the state estimator. Finally, a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones.     

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

Stability Analysis of Stochastic Fuzzy Cellular Neural Networks With Time-Varying Delays and Reaction-Diffusion Terms

In this paper, a class of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms is investigated. By using Lyapunov–Krasovskii functional and stochastic analysis approaches, new and less conservative delay-derivative-dependent stability criteria are presented to guarantee the neural networks to be globally exponentially stable in the mean square for all admissible stochastic perturbations. Numerical simulations are carried out to illustrate the main results.     

联想记忆神经网络局部指数稳定的充要条件及特征函数

讨论非线性连续联想记忆神经网络平衡点局部指数稳定的判定条件及平衡点指数 吸引域的估计,得到了平衡点局部指数稳定的充要条件,并引入一个特征函数,可以判定平衡 点的邻域是否为指数吸引域.文中给出一族范数下(所有单调范数)网络局部或全局指数稳定 的判定条件,推广了已知文献在特定范数下所得到的结论.     

Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements

This paper addresses the problem of output feedback stabilization for nonlinear systems with sampled and delayed output measurements. Firstly, sufficient conditions are proposed to ensure that a class of hybrid systems are globally exponentially stable. Then, based on the sufficient conditions and a dedicated construction continuous observer, an output feedback control law is presented to globally exponentially stabilize the nonlinear systems. The output feedback stabilizer is continuous and hybrid, and can be derived without discretization. The maximum allowable sampling period and the maximum delay are also given. At last, a numerical example is provided to illustrate the design methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Equivalence between local exponential stability of the uniqueequilibrium point and global stability for Hopfield-type neural networkswith two neurons

Fang and Kincaid (1996) proposed an open problem about the relationship between the local stability of the unique equilibrium point and the global stability for a Hopfield-type neural network with continuously differentiable and monotonically increasing activation functions. As a partial answer to the problem, in the two-neuron case it is proved that for each given specific interconnection weight matrix, a Hopfield-type neural network has a unique equilibrium point which is also locally exponentially stable for any activation functions and for any other network parameters if and only if the network is globally asymptotically stable for any activation functions and for any other network parameters. If the derivatives of the activation functions of the network are bounded, then the network is globally exponentially stable for any activation functions and for any other network parameters.