Hopfield neural networks for affine invariant matching

The affine transformation, which consists of rotation, translation, scaling, and shearing transformations, can be considered as an approximation to the perspective transformation. Therefore, it is very important to find an effective means for establishing point correspondences under affine transformation in many applications. In this paper, we consider the point correspondence problem as a subgraph matching problem and develop an energy formulation for affine invariant matching by a Hopfield type neural network. The fourth-order network is investigated first, then order reduction is done by incorporating the neighborhood information in the data. Thus we can use the second-order Hopfield network to perform subgraph isomorphism invariant to affine transformation, which can be applied to an affine invariant shape recognition problem. Experimental results show the effectiveness and efficiency of the proposed method.     

Hopfield网络的全局指数稳定性

在研究Hopfield神经网络时通常都假设输出响应函数是光滑的增函数.但实际应用中遇到的大多数函数都是非光滑函数.因此,本文将通常论文中Hopfield神经网络的输出响应函数连续可微的假设削弱为满足L ipschitz条件.通过引入Lyapunov函数的方法,证明了Hopfield神经网络全局指数收敛的一个充分性定理.并且由此定理获得该类网络全局指数稳定的几个判据.这定理与判据是近期相应文献主要结果的极大改进.     

Convergence of discrete delayed Hopfield neural networks

The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode.     

带有时滞的随机区间Hopfield神经网络的指数稳定性

讨论了带有可变时滞的随机区间Hopfield神经网络的指数稳定性, 利用It^o公式和Lyapunov函数, 得到了几个关于其指数稳定时滞无关和时滞相关的充分性条件, 推广了现有文献中关于定常时滞随机神经网络及其确定形式的许多结果.     

Global exponential stability of Hopfield neural networks

In this article, some sufficient criteria are derived for the global exponential stability of the equilibrium of Hopfield neural networks of the form C_i du_i /dt     

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.     

System dynamics simulation of Hopfield neural networks

Hopfield networks are a class of neural network models where non-linear graded response neurons organized into networks with effectively symmetric synaptic connections are able to implement interesting algorithms, thereby introducing the concept of information storage in the stable states of dynamical systems. In addition to opening up the possibility of using system dynamics as a vehicle to gain potentially useful insights into the behaviour of such networks, especially in the field or nonelectrical engineering, we study the dynamics of the state-space trajectory as well as time domain evolution of sensitivities of the states with respect to circuit parameters.     

Warm start by Hopfield neural networks for interior point methods

Hopfield neural networks and interior point methods are used in an integrated way to solve linear optimization problems. The Hopfield network gives warm start for the primal–dual interior point methods, which can be way ahead in the path to optimality. The approaches were applied to a set of real world linear programming problems. The integrated approaches provide promising results, indicating that there may be a place for neural networks in the “real game” of optimization.     

受扰Hopfield神经网络L2增益稳定性分析

运用研究控制系统有限增益稳定的方法，讨论受扰Hopfield神经网络关于扰动的增益L2稳定，所给条件不但保证受扰网络L2增益稳定，且总能保证网络未受扰时唯一平衡点的存在性和全局渐近稳定性，文中结论还包含从扰动到状态的L2增益估计，它们用网络有关参数明确表达。     

A modified Hopfield neural networks model for graphs-based kinematic structure design

Graph theory can be used efficiently for both kinematic and dynamics analysis of mechanical structures. One of the most important and difficult issues in graphs theory-based structures design is graphs isomorphism discernment. The problem is vital for graph theory-based kinematic structures enumeration, which is known to be nondeterministic polynomial-complete problem. To solve the problem, a Hopfield neural networks (HNN) model is presented and some operators are improved to prevent premature convergence. By comparing with genetic algorithm, the computation times of the HNN model shows less affection when the number of nodes were enhanced. It is concluded that the algorithm presented in this paper is efficient for large-scale graphs isomorphism problem.     

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay.Some Lyapunov-Krasovskii functionals are constructed and the linear matrix inequality(LMI)approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence,uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties.By using Leihniz-Newton formula,free weighting matrices are employed to express this relationship,which implies that the new criteria are less conservative than existing ones.Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.     

Robust stability for interval Hopfield neural networks with time delay.

The conventional Hopfield neural network with time delay is intervalized to consider the bounded effect of deviation of network parameters and perturbations yielding a novel interval dynamic Hopfield neural network (IDHNN) model. A sufficient condition related to the existence of unique equilibrium point and its robust stability is derived.     

Almost periodic solutions for Hopfield neural networks with continuously distributed delays

In this paper Hopfield neural networks with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results.     

动态未知环境下一种Hopfield神经网络路径规划方法

针对动态未知环境下移动机器人路径规划问题,采用一种有效的局部连接Hopfiled神经网络(Hopfield Neural Networks,HNN)来表示机器人的工作空间.机器人在HNN所形成的动态数值势场上进行爬山搜索法来形成避碰路径,并且不存在非期望的局部吸引点.HNN权值设计中考虑了路径安全性因素,通过在障碍物附件形成局部虚拟排斥力来形成安全路径.HNN的连接权是非对称的,并且考虑了信号传播时延.分析了HNN的稳定性,所给稳定性条件和时延无关.HNN模型中突出了最大传播激励,从而使得HNN具有更广的稳定性范围并能表示具有更多节点的机器人工作空间.为对该HNN有效仿真求解,结合约束距离变换和HNN的时延性,给出了单处理器上高效的串行模拟方案,规划路径的时间复杂度为O(N)(N是HNN中神经元的数目),使得路径重规划能快速在线进行.仿真和实验表明该方法的有效性.     

Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks

In this paper, an easy and efficient method is brought forward to design the feedback control for the synchronization of two multiple time-delayed chaotic Hopfield neural networks, whose activation functions and delayed activation functions can have different forms of mapping. Without many complex restrictions and Lyapunov analytic process, the feedback control is given based on the M-matrix theory, the system parameters and the feedback section coefficients. All the results are simulated by Matlab and Simulink, which shows the simplicity and validity of the control. As shown in the simulation results, the error systems converge to zero rapidly.     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

用连续Hopfield网络实现无限时域上的最优控制

为避免直接采用Riccati方程求解时变系统无限域最优控制问题时的计算困难,本文提出一种基于时间连续状态连续型Hopfield网络(CTCSHNN)实现无限域动态最优控制的方法．该方法通过建立CTCSHNN能量函数与移动域控制指标间的等价关系,可在线构建CTCSHNN．理论分析表明,依据该方法设计的CTCSHNN具有稳定性,而且移动域控制量可由网络稳态输出直接产生．将该方法与滚动优化策略相结合,可实现无限时域上的闭环最优控制．仿真实验验证了理论设计的正确性与采用基于CTCSHNN的移动域控制实现无限域闭环最优控制的可行性．     

利用离散Hopfield网络的码本设计方法

论文提出了一种利用Hopfield网络的码本设计方法,分析了LBG算法和离散Hopfield网络的特点,针对该特点构造聚类表格,并按离散Hopfield神经网络串行方式运行,从而得到最终码字集。通过实验表明,在码本大小相同的情况下,峰值信噪比提高了2.742～3.825 dB,生成的码本质量较传统的LBG算法更加有效。     

一种基于无源性理论的模糊Hopfield神经网络学习律设计方法

本文研究了一类模糊Hopfield神经网络系统的稳定性问题.首先,基于无源性理论,设计了一种新的权重学习律,并通过构造的模糊Lyapunov函数证明了系统从输入到输出是无源的.在此基础上,证明了系统在该学习律下是输入到状态稳定的.相比于传统的公共Lypaunov函数,本文所提的模糊Lyapunov函数能保证系统具有更好的性能.最后,通过数值仿真验证了所提方法的有效性.     

一种Hopfield神经网络能量函数改进下的作业车间调度*

由于作业车间调度问题的目标函数目前还无法用换位矩阵的元素以数学公式的形式表示,因此无法保证求出全局最优解。文中首先对换位矩阵表示方法进行了改进,给出新的带有目标函数的能量函数表达式,然后提出改进的Hopfield神经网络作业车间调度方法,并将模拟退火应用于Hopfield神经网络求解,避免了陷入局部极值。仿真结果表明,该方法具有全局搜索能力,并能够保证神经网络的稳态输出为全局最优或近似全局最优。