Mean square stability of recurrent neural networks with random delay and Markovian switching

To establish easily proved conditions under which the random delayed recurrent neural network with Markovian switching is mean-square stability,the evolution of the delay was modeled by a continuous-time homogeneous Markov process with a finite number of states.By employing Lyapunov-Krasovskii functionals and conducting stochastic analysis,a linear matrix inequality (LMI) approach was developed to derive the criteria for mean-square stability,which can be readily checked by some standard numerical packages such as the Matlab LMI Toolbox.A numerical example was exploited to show the usefulness of the derived LMI-based stability conditions.     

多时变时滞细胞神经网络的全局渐近稳定

研究了多时变时滞细胞神经网络的全局渐近稳定问题。给出了多时变时滞细胞神经网络平衡点唯一性和全局渐近稳定的几个新充分判据。所研究的网络模型扩展了现有的同类网络模型,而且所得到的这些新稳定判据考虑了神经元激励和抑制的影响,且能够表示成线性矩阵不等式的形式,易于用现有的内点算法等方法验证。通过2个注释说明了所得结果的有效性。     

Adaptive learning with guaranteed stability for discrete-time recurrent neural networks

To avoid unstable learning, a stable adaptive learning algorithm was proposed for discrete-time recurrent neural networks. Unlike the dynamic gradient methods, such as the backpropagation through time and the real time recurrent learning, the weights of the recurrent neural networks were updated online in terms of Lyapunov stability theory in the proposed learning algorithm, so the learning stability was guaranteed. With the inversion of the activation function of the recurrent neural networks, the proposed learning algorithm can be easily implemented for solving varying nonlinear adaptive learning problems and fast convergence of the adaptive learning process can be achieved. Simulation experiments in pattern recognition show that only 5 iterations are needed for the storage of a 15×15 binary image pattern and only 9 iterations are needed for the perfect realization of an analog vector by an equilibrium state with the proposed learning algorithm.     

不确定区间时滞Markov跳变BAM神经网络的鲁棒指数稳定性

讨论了具有不确定区间时滞的BAM神经网络的鲁棒均方指数稳定性问题。通过构造适当的Lya-punov-Krasovskii泛函,利用一些新的定界技术,以线性矩阵不等式形式给出了Markov跳变BAM神经网络的时滞且区间相关的全局鲁棒指数稳定性判据,该判据利用Matlab的LMI工具很容易进行检验。给出数值示例,说明了判据的有效性与优越性。     

具有混合时滞模糊神经网络的全局指数稳定性分析

主要研究一类具有混合时滞的模糊神经网络.运用不动点定理,M-矩阵理论和一些分析技术,得到了唯一平衡点存在和全局指数稳定的充分条件.实例证明了所得结果的有效性.     

一类神经网络的Ｌａｇｒａｎｇｅ全局指数稳定性

考虑3种不同的有界激励函数,利用Lyapunov函数法和不等式分析技巧,研究了一类具有变时滞的中立型Cohen-Grossberg神经网络的Lagrange全局指数稳定性,并给出了系统模型具有全局指数吸引集的构造性证明：研究结果既适用于分析单稳态系统也适用于多稳态系统;最后通过数值算例及仿真对结果进行了验证．     

时变时滞双向联想记忆神经网络的鲁棒稳定性

通过构造适当的Lyapunov泛函分析了一类时变时滞双向联想记忆神经网络的平衡点稳定性问题。不要求激励函数的单调性和可微性,得到了保证时变时滞双向联想记忆神经网络的平衡点全局鲁棒渐近稳定的两个新判据。所得到的结果能够表示成线性矩阵不等式形式,进而易于用内点算法等方法来验证。通过仿真例子与其他文献中的一些结果进行比较,表明了本文所得结果的有效性。     

滞后细胞神经网络的鲁棒无源分析

考虑了多胞不确定性滞后细胞神经网络(DCNNs)的无源分析问题。基于近期研究成果和线性矩阵不等式(LMI)技术,给出了一个判定DCNNs无源性的新准则,这个新的准则实现了DCNNs系统矩阵和Lyapunov矩阵的完全分离。当DCNNs所受不确定性为多胞类型的不确定性时,该准则相对于基于二次稳定框架的准则而言,可以降低保守性。数值算例揭示了本文方法的有效性。     

Exponential stability and periodic solutions of delayed cellular neural networks

A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi>0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.     

Asymptotical mean square stability of cellular neural networks with random delay

In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results.     

反馈神经网络对非自治的非线性离散系统的近似能力

人工神经网络理论是解决非线性问题的有力工具。章研究了离散型反馈神经网络模型的建立，基于带有输入的非线性离散系统的输出可以被一类反馈神经网络输出神经元的状态向量任意逼近，笔将已有的反馈神经网络近似非线性离散系统的能力从定常系统推广到时变系统，对反馈神经网络近似非线性离散系统的能力进行了扩展研究，针对于更普遍的非自治的非线性离散系统，证明了它们在有限时间段内的输出轨迹可以被反馈神经网络输出神经元的状态向量近似到任何程度。     

离散时滞标准神经网络模型的鲁棒稳定性分析

研究了离散时滞标准神经网络模型（SNNM）的鲁棒渐进稳定性和指数稳定性问题,结合Lyapunov稳定性理论和S方法推导出了两种稳定性的充分条件.所得到的稳定性条件被表示为线性矩阵不等式形式,便于求解.特别的,将鲁棒指数稳定性问题转化为一个广义特征值问题,除了可以判断网络的指数稳定性,还可以方便地估计其最大指数收敛率.在数值示例中,将两类递归神经网络（RNNs）转化为SNNM的形式并利用得到的相关结论对其鲁棒稳定性进行了分析,仿真结果验证了稳定性判据的有效性.SNNM为分析递归网络提供了新的思路,简单且有效.     

具有区间时变时滞的中立型系统稳定性分析

针对一类具有区间时变时滞的线性中立型系统,基于Lyapunov-Krasovskii泛函与改进的自由权矩阵方法,提出时滞区间依赖型稳定性条件.当时滞的变化率已知时,得到同时依赖于时滞区间和时滞变化率的稳定性条件;当时滞的变化率未知时,得到依赖于时滞区间、独立于时滞变化率的稳定性条件.所给条件进一步推广到具有范数有界不确定性的中立型系统,提出鲁棒稳定性条件.所有结果均以线性矩阵不等式的形式给出,利用线性矩阵不等式(LMI)工具求解非常方便.数值实例验证了结果的有效性.     

神经网络的并行稳定性研究

在不涉及能量函数概念的前提下，该文用初等的方法研究了联接矩阵在非负定、非正定、对称和反对称这４种情况下，对应的神经网络在并行运行方式下的收敛特性。对非对称联接的神经网络，该文讨论了将其对称化的条件。     

具有变系数和变时滞的BAM神经网络的全局指数稳定性的新判据

研究了一类具有变系数和变时滞的联想记忆神经网络的全局指数稳定性。通过选择适当的Lyapunov—krasovskii泛函,利用不等式技巧给出了联想记忆神经网络的全局指数稳定性的新判据。     

变时滞神经网络的时滞相关全局渐近稳定新判据

研究了变时滞神经网络的时滞相关渐近稳定性问题。利用Lyapunov-Krasovskii泛函和积分等式方法,提出了此类神经网络有唯一稳定点和全局渐近稳定的充分条件。与已有文献相比,不再要求激活函数单调,并且时滞导数可以不小于1,具有较弱的保守性。算例验证了所给方法的正确性。     

基于LMI的离散时滞切换系统反馈镇定

针对一类子系统为离散时滞系统的切换系统，提出了一种系统稳定性与反馈镇定的控制方法.通过状态变量的转换，将时滞切换系统变为不含时滞项的切换系统.在系统中增加等式约束，将具有双线性矩阵不等式（BMI）形式的综合问题转换为线性矩阵不等式（LMI）的凸优化问题.在任意切换信号作用下离散线性切换系统渐近稳定理论基础上，以线性矩阵不等式形式给出了离散时滞切换系统渐近稳定的充分性条件，并且给出了切换系统状态反馈镇定和输出反馈镇定的控制器设计方法.两个数值算例结果表明，所设计控制方法是可行的，在控制方法的作用下，闭环系统是渐近稳定的.     

时滞中立型神经网络全局渐近稳定性

针对具有时变时滞的中立型Hopfield神经网络,在对时变时滞的合理假设下,文中通过构造适当的Lyapunov泛函,提出了一种新的方法判定时变时滞中立型Hopfield神经网络系统的全局一致渐近稳定性。所得判据是建立在一个代数Riccati方程及其对应离散Lyapunov方程存在对称正定解之上的,并得出了易于计算机仿真实现的线性矩阵不等式的判据形式,仿真验证了结果的有效性。     

Fuzzy logic systems are equivalent to feedforward neural networks

Fuzzy logic systems and feedforward neural networks are equivalent in essence. First, interpolation representations of fuzzy logic systems are introduced and several important conclusions are given. Then three important kinds of neural networks are defined, i.e. linear neural networks, rectangle wave neural networks and nonlinear neural networks. Then it is proved that nonlinear neural networks can be represented by rectangle wave neural networks. Based on the results mentioned above, the equivalence between fuzzy logic systems and feedforward neural networks is proved, which will be very useful for theoretical research or applications on fuzzy logic systems or neural networks by means of combining fuzzy logic systems with neural networks.     

基于鲁棒稳定高阶动态神经网络的非线性系统的辨识

将高阶动态神经网络作为非线性系统的辨识模型,运用Lyapunov稳定性理论,提出一种有效的鲁棒稳定学习规则及相应的学习网络结构,从而确保在对非线性系统辨识时,即使存在建模偏差,辨识误差和动态神经网络的参数能一致最终有界(UUB)稳定,解决了动态神经网络的学习稳定性问题．仿真结果也证明了该辨识方法的有效性．