二阶神经网络的全局指数稳定性分析

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,二阶神经网络较一般神经网络具有更快的收敛速度,对于二阶连续型Hopfield神经网络,用Lyapunov方法讨论平衡点的全局指数稳定性,给出了平衡点全局指数稳定的几个判别准则,作为特例,获得了连续型Hopfield神经网络全局指数稳定的新判据。     

时滞连续Hopfield神经网络的全局指数稳定性

本文采用非线性时滞微分不等式分析技巧,研究了时滞连续Hopfield神经网络的稳定性,给出在任意外界恒常输入下连续Hopfield网络的平衡态的收敛速度及全局指数稳定的若干充分判据.     

一类变时滞神经网络的全局指数稳定性

在不要求激活函数有界的前提下,利用Lyapunov泛函方法和线性矩阵不等式(LMI)分析技巧,研究了一类变时滞神经网络平衡点的存在性和全局指数稳定性.给出判别网络全局指数稳定性的判据,推广了现有文献中的一些结果.这些判据具有LMI的形式,进而易于验证.仿真例子表明了所得结果的有效性.     

一类推广的二元神经网络的稳定性分析

利用不动点定理和微分不等式的分析技巧,引入多个变时滞,去掉对激活函数光滑性与有界性的假设,研究了一类推广的二元神经网络的平衡点的存在性,得到了系统存在平衡点和全局指数稳定性的新的充分条件．     

一类广义时变时滞神经网络的动态分析

讨论了一类广义时变时滞递归神经网络的平衡点的存在性、唯一性和全局指数稳定性。这个神经网络模型包括时滞Hopfield神经网络,时滞Cellular神经网络,时滞Cohen-Grossberg神经网络作为特例。基于微分不等式技术,利用Brouwer不动点定理并构造合适的Lyapunov函数,得到了保证递归神经网络的平衡点存在、唯一、全局指数稳定的新的充分条件。新的充分条件不要求激励函数的可微性、有界性和单调性,同时减少了对限制条件的要求。两个仿真例子表明了所得结果的有效性。     

变时滞神经网络的全局指数稳定性

利用M矩阵理论,同构理论以及不等式技巧,研究了一类变时滞神经网络平衡点的存在性和惟一性问题。同时利用M矩阵理论,反证法以及不等式技巧,得到了变时滞神经网络系统惟一的平衡点的全局指数稳定性的充分条件。通过判断由神经网络的权系数、自反馈函数以及激励函数构造的矩阵是否为M矩阵,即可以检验该变时滞神经网络系统的全局指数稳定性。该判据易于用Matlab进行检验,最后给出一个仿真示例进一步证明了判据的有效性。     

一类时滞神经网络的全局指数稳定性

利用M-矩阵和拓扑学等有关知识，通过构建向量李雅普诺夫函数，研究了一类包含分布时滞和可变时滞的神经网络的平衡点的存在性、唯一性及其全局指数稳定性。在没有假定激励函数有界、可微的情况下，得到了该类神经网络平衡点的存在性、唯一性及其在平衡点全局指数稳定的充分判据。该判据计算简便，且与时间滞后量无关，便于在实践中应用。文中给出了一个算例。     

一类具有变时滞的Hopfield型神经网络的全局指数稳定性

通过构造适当的Lyapunov函数,利用Halanay不等式和Young不等式,讨论一类具有变时滞的Hopfield型神经网络的全局指数稳定性.在对网络施加两个不同的神经元激励函数的条件下,导出网络全局指数稳定的一个充分条件,得到的充分条件在实际应用中易于验证,且有较小的保守性,因而对网络的应用和设计具有重要意义.最后,一个数值实例进一步验证结果的正确性.     

Hopfield神经网络系统的全局稳定性分析

研究一类Hopfield神经网络系统的平衡状态的存在性、唯一性与全局稳定性, 这类系统放弃了以前对激励函数的有界性、单调性和可微性要求. 利用M矩阵理论, 通过构造适当的Lyapunov函数, 得到了系统全局渐近稳定的充分条件.     

一类中立型时滞神经网络的全局渐近稳定性

讨论了一类带有时滞的中立型神经网络的稳定性问题。通过构造Lyapunov-Krasovskii泛函,利用矩阵Schur补性质研究了此类中立型时滞神经网络模型的全局渐近稳定性,得出基于矩阵特征值的稳定性的充分判据,并给出基于矩阵特征值的时滞Hopfield神经网络全局渐近稳定性的充分条件;数值仿真检验了结果的有效性。     

On Robust Exponential Periodicity of Interval Neural Networks with Delays

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the periodic solution of interval-delayed neural networks with periodic input are obtained. All the results obtained are generalizations of some resent results reported in the literature for neural networks with constant input.     

State estimation for delayed neural networks

In this letter, the state estimation problem is studied for neural networks with time-varying delays. The interconnection matrix and the activation functions are assumed to be norm-bounded. The problem addressed is to estimate the neuron states, through available output measurements, such that for all admissible time-delays, the dynamics of the estimation error is globally exponentially stable. An effective linear matrix inequality approach is developed to solve the neuron state estimation problem. In particular, we derive the conditions for the existence of the desired estimators for the delayed neural networks. We also parameterize the explicit expression of the set of desired estimators in terms of linear matrix inequalities (LMIs). Finally, it is shown that the main results can be easily extended to cope with the traditional stability analysis problem for delayed neural networks. Numerical examples are included to illustrate the applicability of the proposed design method.     

Global Output Convergence of a Class of Recurrent Delayed Neural Networks with Discontinuous Neuron Activations

This paper studies the global output convergence of a class of recurrent delayed neural networks with time-varying inputs. We consider non-decreasing activations which may also have jump discontinuities in order to model the ideal situation where the gain of the neuron amplifiers is very high and tends to infinity. In particular, we drop the assumptions of Lipschitz continuity and boundedness on the activation functions, which are usually required in most of the existing works. Due to the possible discontinuities of the activations functions, we introduce a suitable notation of limit to study the convergence of the output of the recurrent delayed neural networks. Under suitable assumptions on the interconnection matrices and the time-varying inputs, we establish a sufficient condition for global output convergence of this class of neural networks. The convergence results are useful in solving some optimization problems and in the design of recurrent delayed neural networks with discontinuous neuron activations.     

Some multistability properties of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions

Multistability is an important dynamical property in neural networks in order to enable certain applications where monostable networks could be computationally restrictive. This paper studies some multistability properties for a class of bidirectional associative memory recurrent neural networks with unsaturating piecewise linear transfer functions. Based on local inhibition, conditions for globally exponential attractivity are established. These conditions allow coexistence of stable and unstable equilibrium points. By constructing some energy-like functions, complete convergence is studied.     

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.     

Couette-Taylor流系统的低模分析及全局稳定性与同步的研究

研究Couette-Taylor流三模Lorenz系统的部分动力学行为与仿真问题,并解释了对应的Couette-Taylor流的演化过程.给出了此三模系统的全局吸引集和正向不变集,得出两个三模系统全局指数同步结果,并利用仿真加以验证.     

Multi-objective optimization of a welding process by the estimation of the Pareto optimal set

The joining of Advanced High Strength Steel (AHSS) Martensitic type is being introduced in automotive industry; however, the optimization of the welding process is required to meet customer quality requirements. Two neural networks are built for modeling the relationship between the welding parameters and the output response of the process. An evolutionary algorithm is used for multi-objective optimization considering the neural networks as objective functions. The results consist of a set of solutions that approximate the Pareto optimal set. The related response of this set is known as the Pareto front. The set of solutions are validated in the real process satisfying the security and quality requirements.     

On the analysis of neural networks with asymmetric connectionweights or noninvertible transfer functions

This paper extends the energy function to the analysis of the stability of neural networks with asymmetric interconnections and noninvertible transfer functions. Based on the new energy function, stability theorems and convergent criteria are derived which improve the available results in the literature. A simpler proof of a previous result for complete stability is given. Theorems on complete stability of neural networks with noninvertible output functions are presented.     

前向傅立叶神经网络系统逼近理论及学习算法

定义了傅立叶神经元与傅立叶神经网络,将一组傅立叶基三角函数作为神经网络各隐层单元的激合函数,设计出一类单输入单输出三层前向傅立叶神经网络与双输入单输出四层前向傅立叶神经网络,以及奇、偶傅立叶神经网络,基于三角函数逼近论,讨论了前向傅立叶神经网络的三角插值机理及系统逼近理论,且有严格的数学理论基础,给出了前向傅立叶神经网络学习算法,通过学习,它们分别能逼近于给定的傅立叶函数到预定的精度。仿真实验表明,该学习算法效率高,具有极为重要的理论价值和应用背景。     

Exponential periodicity and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays

In this paper, the exponential periodicity and stability of neural networks with Lipschitz continuous activation functions are investigated, without assuming the boundedness of the activation functions and the differentiability of time-varying delays, as needed in most other papers. The neural networks contain reaction-diffusion terms and both variable and unbounded delays. Some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique. Furthermore, the exponential converging index is also estimated. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of neural networks with variable and/or unbounded delays. The results extend some previous results. Two examples are given to show the effectiveness of the obtained results.