Improved results on passivity analysis of discrete-time stochastic neural networks with time-varying delay

The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay was investigated. The delay-dependent sufficient criteria were derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. A numerical example is given to show the effectiveness and the benefits of the proposed method.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

Attractors and the attraction basins of discrete-time cellular neural networks

The dynamic behavior of discrete-time cellular neural networks(DTCNN), which is strict with zero threshold value, is mainly studied in asynchronous mode and in synchronous mode. In general, a k-attractor of DTCNN is not a convergent point. But in this paper, it is proved that a k-attractor is a convergent point if the strict DTCNN satisfies some conditions. The attraction basin of the strict DTCNN is studied, one example is given to illustrate the previous conclusions to be wrong, and several results are presented. The obtained results on k-attractor and attraction basin not only correct the previous results, but also provide a theoretical foundation of performance analysis and new applications of the DTCNN.

Stability analysis of extended discrete-time BAMneural networks based on LMI approach

We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory （BAM） neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model - standard neural network model （SNNM）. For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities （LMIs）. We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.

Augmented Lyapunov Approach to Exponential Stability of Discrete-Time Neural Networks

This paper addresses the problem of robust stability for a class of discrete-time neural networks with time-varying delay and parameter uncertainties.By constructing a new augmented Lyapunov-Krasovskii function,some new improved stability criteria are obtained in forms of linear matrix inequality（LMI） technique.Compared with some recent results in the literature,the conservatism of these new criteria is reduced notably.Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

EXPONENTIAL STABILITY OF DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH DELAYS

In this paper, a new sufficient condition for the global exponential stability of a unique equilibrium point of discrete-time cellular neural networks is given. It is shown that the condition relies on the feedback matrices and is independent of the delay parameter. Furthermore, this condition is less restrictive than those given in the literature.

ASYMPTOTICAL STABILITY OF NON-AUTONOMOUS DISCRETE-TIME NEURAL NETWORKS WITH GENERALIZED INPUT-OUTPUT FUNCTION

In this paper, we first introduce the model of discrete-time neural networkswith generalized input--output function and present a proof of the existence of afixed point by Schauder fixed-point principle. Secondly, we study the uniformlyasymptotical stability of equilibrium in non-autonomous discrete--time neuralnetworks and give some sufficient conditions that guarantee the stability of itby using the converse theorem of Lyapunov function. Finally, several examplesand numerical simulations are given to illustrate and reinforce our theories.

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.

BI-DIRECTIONAL COHEN-GROSSBERG NEURAL NETWORK WITH DISCRETE TIME

Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monotonicity, boundedness and differentiability of the activation function.

具有变时滞离散Cohen-Grossberg神经网络的周期解

讨论了具有变时滞离散Cohen-Grossberg神经网络模型,利用M-矩阵理论与适合Lypunov函数,得到该类模型周期解的存在性与全局指数稳定性,推广了先前的结果.

具有脉冲和变时滞的离散Cohen-Grossberg神经网络的全局指数同步

研究了一类具有脉冲和变时滞的离散Cohen-Grossberg神经网络全局指数同步问题.利用ρ-锥理论和微分不等式分析技巧,获得了保证其误差系统全局指数稳定的充分条件,同时也给出了同步指数收敛速率的估计.最后,列举一个例子表明我们所得结果的有效性.

基于DBN-DNN的离散制造车间订单完工期预测方法

准确的订单完工期预测是离散制造车间生产计划制定、调度排产、产品按时交付的重要保证。基于海量的多源制造数据,设计了一种基于深度置信网络—深度神经网络(DBN-DNN)的预测模型,用于实现具有大数据特征的制造系统订单完工期快速预测。选取ReLU为激活函数训练深度置信网络以提取特征,完成预训练;将预训练网络的权重和偏置参数传递至深度神经网络作为预测模型的初始化参数,并增加dropout和L2正则化,避免预测模型的过拟合问题。以某航天机加车间的10000条具有1059个特征的样本为数据集进行了数值实验,通过与多隐含层反向传播神经网络、主成分分析和反向传播神经网络的结合、主成分分析和支持向量回归的结合3种常用预测模型的对比分析,验证了所建立的预测模型在准确度和适用性方面具有更优的性能。

一类变时滞离散Cohen-Grossberg神经网络模型周期解的存在性及其指数稳定性

利用重合度理论研究了一类变时滞的离散Cohen-Grossberg神经网络模型的周期解,并得到了模型周期解的全局指数稳定性的充分条件,推广了已有的结果,为神经网络的应用提供了重要的理论基础.最后给出一个例子进行数值模拟,数值模拟的结果更好地验证了结论.

具有混合时滞的脉冲离散Cohen-Grossberg神经网络的渐近行为

研究了一类具有混合时滞的脉冲离散Cohen-Grossberg神经网络的渐近行为.通过构造一个新的时滞不等式和利用"ρ-锥"理论,获得该神经网络全局吸引集和准不变集的充分条件.

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.

离散分数阶神经网络的全局Mittag-Leffler稳定性

研究了一类离散分数阶神经网络的Mittag-Leffler稳定性问题.首先,基于离散分数阶微积分理论、神经网络理论,提出了一类离散分数阶神经网络.其次,利用不等式技巧和离散Laplace变换,通过构造合适的Lyapunov函数,得到了离散分数阶神经网络全局Mittag-Leffler稳定的充分性判据.最后,通过一个数值仿真算例验证了所提出理论的有效性.

Fault detection for nonlinear discrete-time systems via deterministic learning

Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions （i.e., the internal dynamics） underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function （RBF） networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.

求解时变非线性方程的Adams-Bashforth离散时间算法

为了更好地解决时变非线性方程(time-varying nonlinear equation,TVNE),设计了一类Adams-Bashforth离散时间算法。首先给出了求解TVNE的连续时间零化神经网络,该神经网络具有指数收敛速度。然后利用线性多步算法将连续时间零化神经网络离散化,提出了一类六步Adams-Bashforth离散时间算法,并利用Jury稳定准则,给出了Adams-Bashforth离散算法步长的有效区间。最后将所提出的算法应用于解决机械臂路径规划问题,得到了较好的数值效果,精度最终可以达到10^(-14)m。