New exponentially convergent state estimation method for delayed neural networks

The problem of designing a globally exponentially convergent state estimator for a class of delayed neural networks is investigated in this paper. The time-delay pattern is quite general and including fast time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. A linear estimator of Luenberger-type is developed and by properly constructing a new Lyapunov–Krasovskii functional coupled with the integral inequality, the global exponential stability conditions of the error system are derived. The unknown gain matrix is determined by solving a delay-dependent linear matrix inequality. The developed results are shown to be less conservative than previously published ones in the literature, which is illustrated by a representative numerical example.     

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.     

Less conservative results of state estimation for delayed neural networks with fewer LMI variables

In this paper, the state estimation problem is investigated for neural networks with time-varying delays as well as general activation functions. By applying the Finsler's Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent conditions are developed to estimate the neuron state with some available output measurements such that the error-state system is global asymptotically stable. It is established theoretically that one special case of the obtained criteria is equivalent to some existing result with same conservatism but including fewer LMI variables. As the present conditions involve no free-weighting matrices, the computational burden is largely reduced. Two examples are provided to demonstrate the effectiveness of the theoretical results.     

Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays

This paper investigates delay-dependent robust asymptotic state estimation of fuzzy neural networks with mixed interval time-varying delay. In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the robust state estimation of Hopfield neural networks with mixed interval time-varying delays. The main purpose 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 asymptotically stable. Based on the Lyapunov-Krasovskii functional which contains a triple-integral term, delay-dependent robust state estimation for such T-S fuzzy Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving a delay-dependent LMI. Finally two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

网络化神经网络的时滞依赖稳定性判据

本文研究了网络化神经网络的稳定性问题.首先,为了利用网络系统的采样特征,定义了一个新的Lyapunov泛函;通过分析网络诱导时延和执行周期之间的关系,采用一个迭代凸组合技术,得到了一个包含较少保守性的稳定性判据.然后,给出一个基于采样数据的神经网络稳定性判据,减少了计算复杂性.最后,通过一个数例,验证了本文方法的有效性和优越性.     

Delay-dependent robust stability analysis for interval linear time-variant systems with delays and application to delayed neural networks

Some delay-dependent robust asymptotical stability criteria for uncertain linear time-variant systems with multiple delays are established by means of parameterized first-order model transformation and the transformation of the interval uncertainty into the norm-bounded uncertainty. The stable regions with respect to the delay parameters are also formulated. Based on these results, we investigate the stability issue of a class of delayed neural networks that can be transformed into linear time-variant systems, and then several new global asymptotical stability criteria are exploited. Numerical examples are presented to illustrate the effectiveness of our results.     

Improved results on state estimation for neural networks with time-varying delays

In this paper, some improved results on the state estimation problem for recurrent neural networks with both time-varying and distributed time-varying delays are presented. Through available output measurements, an improved delay-dependent criterion is established to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable, and the derivative of time-delay being less than 1 is removed, which generalize the existent methods. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed results.     

Delay-dependent exponential state estimators for stochastic neural networks of neutral type with both discrete and distributed delays

This paper considered the state estimation for stochastic neural networks of neutral type with discrete and distributed delays. By using available output measurements, the state estimator can approximate the neuron states, and the asymptotic property of the state error is mean square exponential stable and also almost surely exponential stable in the presence of discrete and distributed delays. Under the Lipschitz assumptions for the activation functions and the measurement nonlinearity, a delay-dependent linear matrix inequality (LMI) criterion is proposed to guarantee the existence of the desired estimators by constructing an appropriate Lyapunov-Krasovskii function. It is shown that the existence conditions and the explicit expression of the state estimator can be parameterised in terms of the solution to a LMI. Finally, two numerical examples are presented to demonstrate the validity of the theoretical results and show that the theorem can provide less conservative conditions.     

Distributed mode-dependent state estimation for semi-Markovian jumping neural networks via sampled data

In this paper, a novel distributed state estimation scheme with sampled data is proposed for the semi-Markovian jumping neural networks (SMJNNs) with time-varying delays. In particular, mode-dependent distributed state estimators are designed to provide more flexibility. Based on the mode-dependent Lyapunov-Krasovskii functional, sufficient criteria are presented for ensuring the existence of the state estimators, based on which the desired mode-dependent estimator gains are further obtained. Finally, an illustrative example is presented for verifying the effectiveness and applicability of our theoretical results.     

Delay-dependent stability analysis for impulsive neural networks with time varying delays

In this paper, the global exponential stability and global asymptotic stability of the neural networks with impulsive effect and time varying delays is investigated. By using Lyapunov–Krasovskii-type functional, the quality of negative definite matrix and Cauchy criterion, we obtain the sufficient conditions for global exponential stability and global asymptotic stability of such model, in terms of linear matrix inequality (LMI), which depend on the delays. Two examples are given to illustrate the effectiveness of our theoretical results.     

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.     

Passivity analysis for delayed discontinuous neural networks

In this paper, we have integrated the passivity of delayed neural networks with discontinuous activations which are unbounded. Based on differential inclusion theory and nonsmooth analysis, some sufficient conditions are presented by means of the generalized Lyapunov method. The results are established in form of linear matrix inequality. In addition, Some numerical examples are proposed to show the effectiveness of the developed results.     

Two approaches to partial-nodes-based state estimation for delayed complex networks with intermittent measurement transmissions

This paper is concerned with the state estimation problem for delayed complex dynamic networks with non-identical local dynamical systems. The state estimation is conducted based on constrained information of the measurement outputs. Specifically, the network outputs are available only from a portion of network nodes, and such outputs are transmitted from the network nodes to the estimator in an intermittent way. By utilizing the Halanay inequality method as well as the average dwell-time approach, two sets of sufficient conditions are established that ensure the error dynamics of the state estimation to converge to zero exponentially, and explicit expressions of the estimator gains are further characterized. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed approaches.     

A Partial-Nodes-Based Information fusion approach to state estimation for discrete-Time delayed stochastic complex networks

This paper is concerned with the information-fusion-based state estimation problem for a class of discrete-time complex networks with time-varying delays and stochastic perturbations. The measurement outputs available for state estimation are from a fraction of network nodes, and the addressed problem is therefore referred to as the so-called Partial-Nodes-Based (PNB) state estimation problem. By employing the Lyapunov stability theory, a novel framework is established to cope with the PNB state estimation problem by the measurement outputs collected from partial network nodes. By constructing specific Lyapunov-Krasovskii functionals, sufficient criteria are derived for the existence of the desired exponentially ultimately bounded state estimator in mean square for the complex networks. Moreover, a special case is considered where the complex network under investigation is free of stochastic perturbations and the corresponding analysis issue is discussed to ensure the existence of an exponential state estimator. In addition, the explicit expressions of the gains of the desired estimators are characterized. Finally, a numerical illustrative example is presented to demonstrate the effectiveness of the obtained theoretical results.     

Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays

This paper investigates the event-triggered state estimation problem of Markovian jumping impulsive neural networks with interval time-varying delays. The purpose is to design a state estimator to estimate system states through available output measurements. In the neural networks, there are a set of modes, which are determined by Markov chain. A Markovian jumping time-delay impulsive neural networks model is employed to describe the event-triggered scheme and the network- related behaviour, such as transmission delay, data package dropout and disorder. The proposed event-triggered scheme is used to determine whether the sampled state information should be transmitted. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. First, we design a state observer to estimate the neuron states. Second, based on a novel Lyapunov-Krasovskii functional (LKF) with triple-integral terms and using an improved inequality, several sufficient conditions are derived. The derived conditions are formulated in terms of a set of linear matrix inequalities , under which the estimation error system is globally asymptotically stable in the mean square sense. Finally, numerical examples are given to show the effectiveness and superiority of the results.     

Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay

In this paper, we focus on the stability problem for discrete-time switched neural networks with time-varying delay resorting to the average dwell time method. In terms of linear matrix inequality approach, a delay-dependent sufficient condition of exponential stability is developed for a kind of switching signal with average dwell time. A numerical example is given to show the validness of the established result.     

Delay-dependent robust stability criteria for delay neural networks with linear fractional uncertainties

This article investigates the problem of robust stability for neural networks with time-varying delays and parameter uncertainties of linear fractional form. By introducing a new Lyapunov-Krasovskii functional and a tighter inequality, delay-dependent stability criteria are established in term of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach. Recommended by Editorial Board member Naira Hovakimyan under the direction of Editor Young-Hoon Joo. This work was supported by the National Science foundation of China under Grant no. 60774013 and Key Laboratory of Education Ministry for Image Processing and Intelligent Control under grant no. 200805. Tao Li received the Ph.D. degree in The Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in Department of Information and Communication, Nanjing University of Information Science and Technology. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Lei Guo received the Ph.D. degree in the Research Institute of Automation Southeast University, China. From 1999 to 2004, he has worked at Hong Kong University, IRCCyN (France), Glasgow University, Loughborough University and UMIST, UK. Now He is a Professor in School of Instrument Science and Opto-Electronics Engineering, Beihang University. His current research interests include robust control, fault detection and diagnosis. Lingyao Wu received the Ph.D. degree in The Research Institute of Automation Southeast University, China. Now He is an Assistant Professor in the Research Institute of Automation Southeast University. His current research interests include time-delay systems, neural networks, robust control, fault detection and diagnosis. Changyin Sun received the Ph.D. degree in the Research Institute of Automation Southeast University, China. Now He is a Professor in the Research Institute of Automation Southeast University. His current research interests include timedelay systems, neural networks.     

Neural networks for nonlinear state estimation

Estimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non-recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.     

Guaranteed performance state estimation of static neural networks with time-varying delay

This paper is concerned with studying two kinds of guaranteed performance state estimation problems for static neural networks with time-varying delay. Both delay-independent and delay-dependent design criteria are presented under which the resulting estimation error system is globally asymptotically stable and a prescribed performance is guaranteed in the H_∞ or generalized H₂ sense. It is shown that the gain matrices of the state estimator and the optimal performance indexes can be simultaneously obtained by solving convex optimization problems subject to linear matrix inequalities. It is worth noting that no slack variable is introduced in the proposed conditions, and thus the computational burden is reduced. The effectiveness of the developed results is finally demonstrated by simulation examples.     

Regularization parameter estimation for feedforward neural networks

Under the framework of the Kullback-Leibler (KL) distance, we show that a particular case of Gaussian probability function for feedforward neural networks (NNs) reduces into the first-order Tikhonov regularizer. The smooth parameter in kernel density estimation plays the role of regularization parameter. Under some approximations, an estimation formula is derived for estimating regularization parameters based on training data sets. The similarity and difference of the obtained results are compared with other work. Experimental results show that the estimation formula works well in sparse and small training sample cases.