Stability analysis of Hopfield-type neural networks

The paper applies several concepts in robust control research such as linear matrix inequalities, edge theorem, parameter-dependent Lyapunov function, and Popov criteria to investigate the stability property of Hopfield-type neural networks. The existence and uniqueness of an equilibrium is formulated as a matrix determinant problem. An induction scheme is used to find the equilibrium. To verify whether the determinant is nonzero for a class of matrix, a numerical range test is proposed. Several robust control techniques in particular linear matrix inequalities are used to characterize the local stability of the neural networks around the equilibrium. The global stability of the Hopfield neural networks is then addressed using a parameter-dependent Lyapunov function technique. All these results are shown to generalize existing results in verifying the existence/uniqueness of the equilibrium and local/global stability of Hopfield-type neural networks.     

&thetas;-adaptive neural networks: a new approach to parameterestimation

A novel use of neural networks for parameter estimation in nonlinear systems is proposed. The approximating ability of the neural network is used to identify the relation between system variables and parameters of a dynamic system. Two different algorithms, a block estimation method and a recursive estimation method, are proposed. The block estimation method consists of the training of a neural network to approximate the mapping between the system response and the system parameters which in turn is used to identify the parameters of the nonlinear system. In the second method, the neural network is used to determine a recursive algorithm to update the parameter estimate. Both methods are useful for parameter estimation in systems where either the structure of the nonlinearities present are unknown or when the parameters occur nonlinearly. Analytical conditions under which successful estimation can be carried but and several illustrative examples verifying the behavior of the algorithms through simulations are presented.     

A new approach to artificial neural networks

A novel approach to artificial neural networks is presented. The philosophy of this approach is based on two aspects: the design of task-specific networks, and a new neuron model with multiple synapses. The synapses' connective strengths are modified through selective and cumulative processes conducted by axo-axonic connections from a feedforward circuit. This new concept was applied to the position control of a planar two-link manipulator exhibiting excellent results on learning capability and generalization when compared with a conventional feedforward network. In the present paper, the example shows only a network developed from a neuronal reflexive circuit with some useful artifices, nevertheless without the intention of covering all possibilities devised.     

Normalized Exponential Neural Networks

In this paper,the normalized exponential neural network(ENN)is studied.It is proved that ENN is a universal approximator.The stability relation between systems and neural networks working as controllers is investigated.The results show that when designing a system,one should firstly Consider system stability rather than controller stability,Accordingly,a new hybrid learning algorithm is presented,and it is proved that this algorithm eventually converge to equilibria.     

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.     

Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.     

Complete delay-decomposing approach to exponential stability for uncertain cellular neural networks with discrete and distributed time-varying delays

This paper considers the problem of exponential stability of uncertain cellular neural networks with discrete and distribute time-varying delays. Some new delay-dependent stability condition are derived in terms of linear matrix inequality. We divide delay interval into multiple segments and employ the free-weighting matrices method to obtained some less conservative criteria. Finally, numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

A new approach to phoneme recognition by phoneme filter neural networks

This paper describes a phoneme filter neural network (PFN) approach to phoneme recognition. Most conventional speech recognition neural networks have a serious drawback: the network output values do not correspond to candidate likelihoods. The PFN is a multilayer neural network with fewer hidden units than input units prepared for each of the phoneme categories. Each network is trained as an identity mapping by speech data belonging to one phoneme category. In the recognition process, the similarity between the input data and output data is computed for each network. The results of the experiment to apply the Japanese vowel recognition task showed that the PFN recognition rates for the top two or more choices are higher than those of a conventional three-layer neural network and the PFN outputs represented candidate likelihoods. It was also confirmed that the PFN had a mapping ability and recognition performance superior to those of the linear K-L transformation method because of the nonlinearity of the PFN.     

Estimate of exponential convergence rate and exponential stabilityfor neural networks

Estimates of exponential convergence rate and exponential stability are studied for a class of neural networks which includes Hopfield neural networks and cellular neural networks. Both local and global exponential convergence are discussed. Theorems for estimation of the exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction in the case of local exponential convergence are obtained. Simple conditions are presented for checking exponential stability of the neural networks.     

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     

A new approach to radial basis function-based polynomial neural networks: analysis and design

In this study, we introduce a new topology of radial basis function-based polynomial neural networks (RPNNs) that is based on a genetically optimized multi-layer perceptron with radial polynomial neurons (RPNs). This paper offers a comprehensive design methodology involving various mechanisms of optimization, especially fuzzy C-means (FCM) clustering and particle swarm optimization (PSO). In contrast to the typical architectures encountered in polynomial neural networks (PNNs), our main objective is to develop a topology and establish a comprehensive design strategy of RPNNs: (a) The architecture of the proposed network consists of radial polynomial neurons (RPN). These neurons are fully reflective of the structure encountered in numeric data, which are granulated with the aid of FCM clustering. RPN dwells on the concepts of a collection of radial basis function and the function-based nonlinear polynomial processing. (b) The PSO-based design procedure being applied to each layer of the RPNN leads to the selection of preferred nodes of the network whose local parameters (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, the number of clusters of FCM clustering, and a fuzzification coefficient of the FCM method) are properly adjusted. The performance of the RPNN is quantified through a series of experiments where we use several modeling benchmarks, namely a synthetic three-dimensional data and learning machine data (computer hardware data, abalone data, MPG data, and Boston housing data) already used in neuro-fuzzy modeling. A comparative analysis shows that the proposed RPNN exhibits higher accuracy in comparison with some previous models available in the literature.     

Nonlinear Poisson regression using neural networks: a simulation study

We describe a novel extension of the Poisson regression model to be based on a multi-layer perceptron, a type of neural network. This relaxes the assumptions of the traditional Poisson regression model, while including it as a special case. In this paper, we describe neural network regression models with six different schemes and compare their performances in three simulated data sets, namely one linear and two nonlinear cases. From the simulation study it is found that the Poisson regression models work well when the linearity assumption is correct, but the neural network models can largely improve the prediction in nonlinear situations.     

Novel criteria for global robust exponential stability of neural networks with time-varying delays via LMI approach

The article addresses the problem of global robust exponential stability of interval neural networks with time-varying delays. On the basis of linear matrix inequality technique and M-matrix theory, some novel sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for delayed interval neural networks are presented. It is shown that our results improve and generalize some previously published ones. Some numerical examples and simulations are given to show the effectiveness of the obtained results.     

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.     

A new classification approach for neural networks hardware: from standards chips to embedded systems on chip

The aim of this paper is to propose a new classification approach of artificial neural networks hardware. Our motivation behind this work is justified by the following two arguments: first, during the last two decades a lot of approaches have been proposed for classification of neural networks hardware. However, at present there is not a clear consensus on classification criteria and performances. Second, with the evolution of the microelectronic technology and the design tools and techniques, new artificial neural networks (ANNs) implementations have been proposed, but they are not taken into consideration in the existing classification approaches of ANN hardware. In this paper, we propose a new approach for classification of neural networks hardware. The paper is organized in three parts: in the first part we review most of existing approaches proposed in the literature during the period 1990–2010 and show the advantages and disadvantages of each one. In the second part, we propose a new classification approach that takes into account most of consensual elements in one hand and in the other hand it takes into consideration the evolution of the design technology of integrated circuits and the design techniques. In the third part, we review examples of neural hardware achievements from industrial, academic and research institutions. According to our classification approach, these achievements range from standard chips to VLSI ASICs, FPGA and embedded systems on chip. Finally, we enumerate design issues that are still posed. This could help to give new directions for future research work.     

Global exponential stability analysis for a class of neural networks with time delays

Employing Brouwer's fixed point theorem, matrix theory, we made a further investigation of a class of neural networks with delays in this paper. A family of sufficient conditions were given for checking global exponential stability. These results have important leading significance in the design and applications of globally stable neural networks with delays. Our results extended and improved some earlier publications. Copyright © 2011 John Wiley & Sons, Ltd.     

A neural networks approach to minority game

The minority game (MG) comes from the so-called “El Farol bar” problem by W.B. Arthur. The underlying idea is competition for limited resources and it can be applied to different fields such as: stock markets, alternative roads between two locations and in general problems in which the players in the “minority” win. Players in this game use a window of the global history for making their decisions, we propose a neural networks approach with learning algorithms in order to determine players strategies. We use three different algorithms to generate the sequence of minority decisions and consider the prediction power of a neural network that uses the Hebbian algorithm. The case of sequences randomly generated is also studied. Research supported by Local Project 2004–2006 (EX 40%) Università di Foggia. A. Sfrecola is a researcher financially supported by Dipartimento di Scienze Economiche, Matematiche e Statistiche, Università degli Studi di Foggia, Foggia, Italy.     

Impulses-induced exponential stability in recurrent delayed neural networks

The present paper formulates and studies a model of recurrent neural networks with time-varying delays in the presence of impulsive connectivity among the neurons. This model can well describe practical architectures of more realistic neural networks. Some novel yet generic criteria for global exponential stability of such neural networks are derived by establishing an extended Halanay differential inequality on impulsive delayed dynamical systems. The distinctive feature of this work is to address exponential stability issues without a priori stability assumption for the corresponding delayed neural networks without impulses. It is shown that the impulses in neuronal connectivity play an important role in inducing global exponential stability of recurrent delayed neural networks even if it may be unstable or chaotic itself. Furthermore, example and simulation are given to illustrate the practical nature of the novel results.     

Absolute exponential stability of a class of continuous-time recurrent neural networks

This paper presents a new result on absolute exponential stability (AEST) of a class of continuous-time recurrent neural networks with locally Lipschitz continuous and monotone nondecreasing activation functions. The additively diagonally stable connection weight matrices are proven to be able to guarantee AEST of the neural networks. The AEST result extends and improves the existing absolute stability and AEST ones in the literature.