Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.

Model algorithm control using neural networks for input delayed nonlinear control system

The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to ＂learn＂the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.

Stability Analysis of Cohen-Grossberg Neural Networks with Time-Varying Delays

The global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals and utilizing differential in-equality techniques, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of the system are obtained. The criteria do not require the activation functions to be differentiable or monotone nondecreasing. Some stability results from previous works are extended and improved. Comparisons are made to demonstrate the advantage of our results.

Global Exponential Convergence of Neutral Type Competitive Neural Networks with D Operator and Mixed Delay

The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.

Periodic Solution for a Complex-Valued Network Model with Discrete Delay

For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathe­matical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.

Discrete-time delayed standard neural network model and its application

A novel neural network model, termed the discrete-time delayed standard neural network model （DDSNNM）, and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks （RNNs） and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed （or non-delayed） nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks （CNNs） and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.

Exponential convergence and stability of delayed fuzzy cellular neural networks with time-varying coefficients

In this paper, the dynamic behaviors of fuzzy cellular neural networks （FCNNs） with time-varying coefficients and delays are considered. Some criteria are established to ensure the exponential convergence or exponential stability of such neural networks. The effectiveness of obtained results is illustrated by a numerical example.

Robust fuzzy control of Takagi-Sugeno fuzzy neural networks with discontinuous activation functions and time delays

The problem of global robust asymptotical stability for a class of Takagi-Sugeno fuzzy neural networks（TSFNN） with discontinuous activation functions and time delays is investigated by using Lyapunov stability theory.Based on linear matrix inequalities（LMIs）,we originally propose robust fuzzy control to guarantee the global robust asymptotical stability of TSFNNs.Compared with the existing literature,this paper removes the assumptions on the neuron activations such as Lipschitz conditions,bounded,monotonic increasing property or the right-limit value is bigger than the left one at the discontinuous point.Thus,the results are more general and wider.Finally,two numerical examples are given to show the effectiveness of the proposed stability results.

Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

Novel Computing for the Delay Differential Two-Prey and One-Predator System

The aim of these investigations is to find the numerical performances of the delay differential two-prey and one-predator system.The delay differential models are very significant and always difficult to solve the dynamical kind of ecological nonlinear two-prey and one-predator system.Therefore,a stochastic numerical paradigm based artificial neural network(ANN)along with the Levenberg-Marquardt backpropagation(L-MB)neural networks(NNs),i.e.,L-MBNNs is proposed to solve the dynamical twoprey and one-predator model.Three different cases based on the dynamical two-prey and one-predator system have been discussed to check the correctness of the L-MBNNs.The statistic measures of these outcomes of the dynamical two-prey and one-predator model are chosen as 13%for testing,12%for authorization and 75%for training.The exactness of the proposed results of L-MBNNs approach for solving the dynamical two-prey and onepredator model is observed with the comparison of the Runge-Kutta method with absolute error ranges between 10−05 to 10−07.To check the validation,constancy,validity,exactness,competence of the L-MBNNs,the obtained state transitions(STs),regression actions,correlation presentations,MSE and error histograms(EHs)are also provided.

Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities

In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak discontinuities.First,the solution interval is divided into multiple subintervals by weak discontinuity points.Then,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each subinterval.Finally,the parameters of the neural network are obtained by training with the extreme learning machine.The numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.

Some Features of Neural Networks as Nonlinearly Parameterized Models of Unknown Systems Using an Online Learning Algorithm

This paper deals with deriving the properties of updated neural network model that is exploited to identify an unknown nonlinear system via the standard gradient learning algorithm. The convergence of this algorithm for online training the three-layer neural networks in stochastic environment is studied. A special case where an unknown nonlinearity can exactly be approximated by some neural network with a nonlinear activation function for its output layer is considered. To analyze the asymptotic behavior of the learning processes, the so-called Lyapunov-like approach is utilized. As the Lyapunov function, the expected value of the square of approximation error depending on network parameters is chosen. Within this approach, sufficient conditions guaranteeing the convergence of learning algorithm with probability 1 are derived. Simulation results are presented to support the theoretical analysis.

On modeling the digital gate delay under process variation

To achieve a characterization method for the gate delay library used in block based statistical static timing analysis with neither unacceptably poor accuracy nor forbiddingly high cost,we found that general-purpose gate delay models are useful as intermediaries between the circuit simulation data and the gate delay models in required forms.In this work,two gate delay models for process variation considering different driving and loading conditions are proposed.From the testing results,these two models,especially the one that combines effective dimension reduction（EDR） from statistics society with comprehensive gate delay models,offer good accuracy with low characterization cost,and they are thus competent for use in statistical timing analysis（SSTA）.In addition, these two models have their own value in other SSTA techniques.

Convergence and Periodicity of Solutions for a Discrete Model

The discrete-time network model of two neurons with function f（u） ={1,u∈[0,σ] 0,U∈[0,σ]is considered. We obtain some sufficient conditions that every solution of system is convergent or periodic.

Neural Network inverse Adaptive Controller Based on Davidon Least Square

General neural network inverse adaptive controller has two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system. These defects limit the scope in which the neural network inverse adaptive controller is used. We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence, and then through constructing the pseudo-plant, a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system. The simulation results show the validity of this scheme.

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model （SNNM）, is advanced to describe some delayed （or non-delayed） discrete-time intelligent systems composed of neural networks and Takagi and Sugeno （T-S） fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities （LMIs） which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based （or fuzzy） discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based （or fuzzy） discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.

Numerical Solutions of a Novel Designed Prevention Class in the HIV Nonlinear Model

The presented research aims to design a new prevention class(P)in the HIV nonlinear system,i.e.,the HIPV model.Then numerical treatment of the newly formulated HIPV model is portrayed handled by using the strength of stochastic procedure based numerical computing schemes exploiting the artificial neural networks(ANNs)modeling legacy together with the optimization competence of the hybrid of global and local search schemes via genetic algorithms(GAs)and active-set approach(ASA),i.e.,GA-ASA.The optimization performances through GA-ASA are accessed by presenting an error-based fitness function designed for all the classes of the HIPV model and its corresponding initial conditions represented with nonlinear systems of ODEs.To check the exactness of the proposed stochastic scheme,the comparison of the obtained results and Adams numerical results is performed.For the convergence measures,the learning curves are presented based on the different contact rate values.Moreover,the statistical performances through different operators indicate the stability and reliability of the proposed stochastic scheme to solve the novel designed HIPV model.

基于TWOA-BP的矿井冲击地压分级预测研究

为提高煤矿开采工作的安全性,准确预测煤矿冲击地压灾害发生,提出冲击地压分级预测的TWOA-BP模型。先通过灰色关联分析法(GRA)筛选冲击地压的影响因素作为TWOA-BP预测模型的输入层,最终确定8项影响因素后,采用鲸鱼算法(WOA)对BP神经网络的权值和阈值进行优化,随后利用Tent混沌映射初始化鲸鱼种群以增加种群多样性,最终解决了BP模型收敛速度慢和易陷入局部极小的问题。研究结果表明:与其他预测模型相比,TWOA-BP方法具有收敛速度快、预测精度高、操作简便等特点。

基于PSO-BP复合网络的掘进机截割部故障智能诊断

针对井下掘进机故障诊断频发,传统诊断方法和BP神经网络诊断周期长的情况,以常村煤矿矿用EBZ-160TY型掘进机为背景,提出基于PSO-BP神经网络模型的掘进机截割部智能诊断模型。该模型能够弥补BP神经网络模型收敛周期长、局部最优搜索差的缺点,实现模型的快速收敛和故障准确预测。通过设置PSO-BP神经网络模型参数、样本数据训练,同时经过数据测试,确定PSO-BP神经网络模型预测结果故障预测率为100%,而BP神经网络的预测精度为80%,且在同时间下,PSO-BP神经网络较BP神经网络预测精度更高。在同精度下,PSO-BP神经网络模型收敛速度更快,在精度为1×10^(-5)时,PSO-BP神经网络模型仅需7步,BP神经网络平均需要198.5步。综合测试结果说明,PSO-BP神经网络模型能够较快实现掘进机故障的预测,且达到较高的预测精度,为掘进机故障诊断提供依据。