Class Of Discrete-time Neural Networks Research Articles

Non-fragile extended dissipative state estimation for delayed discrete-time neural networks: application to quadruple tank process model

This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving uncertainties as well as time-varying delay components. The requisite of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is extended dissipative having external disturbance and unpredictable fragility performance. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), the sufficient conditions for the extended dissipativity performance of the error system obtained by means of the proposed DNNs and its estimator which includes the $$H_{\infty }$$ performance, $$L_{2}-L_{\infty }$$ performance, passivity and dissipativity performance in a unified framework. The established theoretical results are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical softwares. In order to analyze the applicability and effectiveness of the proposed theoretical results, numerical examples including a quadruple tank process (QTP) system model have been illustrated with simulation results.

Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the finite-time H∞ state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H∞ performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.

Robust H∞ Performance of Discrete-time Neural Networks with Uncertainty and Time-varying Delay

In this paper, we are concerned with the robust H∞ problem for a class of discrete-time neural networks with uncertainties. Under a weak assumption on the activation functional, some novel summation inequality techniques and using a new Lyapunov-Krasovskii (L-K) functional, a delay-dependent condition guaranteeing the robust asymptotically stability of the concerned neural networks is obtained in terms of a Linear Matrix Inequality(LMI). It is shown that this stability condition is less conservative than some previous ones in the literature. The controller gains can be derived by solving a set of LMIs. Finally, two numerical examples result are given to illustrate the effectiveness of the developed theoretical results.

Event-triggered [formula omitted]–[formula omitted] state estimation for discrete-time neural networks with sensor saturations and data quantization

The problem of event-triggered L2–L∞ state estimation for a class of discrete-time neural networks with mixed time delays, sensor saturations and data quantization is investigated in this paper. The mixed time delays include discrete and distributed delays. Due to the constraint of physical devices, the measurement outputs are partially nonlinear and subjected to sensor saturations. In order to save the limited communication resource, an adaptive event-triggered mechanism is employed to determine whether or not the current sampled data should be transmitted. Data quantization is also an effective way to decrease the amount of transmitted data via networks. Some delay-dependent sufficient conditions have been derived to guarantee the augmented estimator system is asymptotic stable and achieve the prescribed L2–L∞ performance. The design process of L2–L∞ estimator is also derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Non-fragile finite-time [formula omitted] state estimation for discrete-time neural networks with semi-Markovian switching and random sensor delays based on Abel lemma approach

This paper focuses the non-fragile state estimation problem for a class of discrete-time neural networks with semi-Markov switching and unreliable communication links in finite time l2−l∞ sense that are caused due to the randomly occurring sensor nonlinearity, randomly occurring time delays and packet dropouts. By employing semi-Markovian switching with time-varying transition rates, a broader class of dynamical systems than the traditional Markovian jump linear systems is described. Then, based on the Abel lemma approach on finite sum inequalities, a non-fragile state estimator is obtained to ensure that the resulting error system is mean-square stochastically finite-time stable with a prescribed l2−l∞ performance. Sufficient conditions for the gain of the state estimator are obtained through solving a set of linear matrix inequalities. Finally a numerical example is provided to substantiate the theoretical results.

Robust finite-time state estimation for uncertain discrete-time Markovian jump neural networks with two delay components

Abstract This paper considers the problem of robust finite-time state estimation for a class of discrete-time neural networks with two delay components and Markovian jump parameters. A new discrete-time Lyapunov–Krasovskii functional containing two independent delay components is constructed. Some well-known inequalities are introduced to reduce the conservatism. To ensure the existence of the state estimator, sufficient conditions are derived in the form of linear matrix inequalities, which can be checked easily by the MATLAB LMI toolbox. Finally, an example is given to show the effectiveness of the designed estimator.

Delay-distribution-dependent [formula omitted] state estimation for delayed neural networks with [formula omitted]-dependent noises and fading channels

This paper deals with the H∞ state estimation problem for a class of discrete-time neural networks with stochastic delays subject to state- and disturbance-dependent noises (also called (x,v)-dependent noises) and fading channels. The time-varying stochastic delay takes values on certain intervals with known probability distributions. The system measurement is transmitted through fading channels described by the Rice fading model. The aim of the addressed problem is to design a state estimator such that the estimation performance is guaranteed in the mean-square sense against admissible stochastic time-delays, stochastic noises as well as stochastic fading signals. By employing the stochastic analysis approach combined with the Kronecker product, several delay-distribution-dependent conditions are derived to ensure that the error dynamics of the neuron states is stochastically stable with prescribed H∞ performance. Finally, a numerical example is provided to illustrate the effectiveness of the obtained results.

Optimal Communication Network-Based H∞ Quantized Control With Packet Dropouts for a Class of Discrete-Time Neural Networks With Distributed Time Delay.

This paper is concerned with optimal communication network-based H∞ quantized control for a discrete-time neural network with distributed time delay. Control of the neural network (plant) is implemented via a communication network. Both quantization and communication network-induced data packet dropouts are considered simultaneously. It is assumed that the plant state signal is quantized by a logarithmic quantizer before transmission, and communication network-induced packet dropouts can be described by a Bernoulli distributed white sequence. A new approach is developed such that controller design can be reduced to the feasibility of linear matrix inequalities, and a desired optimal control gain can be derived in an explicit expression. It is worth pointing out that some new techniques based on a new sector-like expression of quantization errors, and the singular value decomposition of a matrix are developed and employed in the derivation of main results. An illustrative example is presented to show the effectiveness of the obtained results.

Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay

This paper is concerned with the stability problem for a class of discrete-time neural networks with time-varying delays in network coupling, parameter uncertainties and time-delay in the leakage term. By constructing triple Lyapunov–Krasovskii functional terms, based on Lyapunov method, new sufficient conditions are established to ensure the asymptotic stability of discrete-time delayed neural networks system. Convex reciprocal technique is incorporated to deal with double summation terms and the stability criteria are presented in terms of linear matrix inequalities (LMIs). Finally numerical examples are exploited to substantiate the theoretical results. It has also shown that the derived conditions are less conservative than the existing results in the literature.

H∞ state estimation for discrete-time delayed neural networks with randomly occurring quantizations and missing measurements

Abstract This paper is concerned with the H ∞ state estimation problem for a class of discrete-time neural networks with time-varying delays, randomly occurring quantizations (ROQs) as well as missing measurements. The phenomena of ROQ and missing measurements are governed by a Bernoulli distributed stochastic sequence. The purpose of the addressed problem is to design a state estimator such that the dynamics of the estimation error is exponentially stable in the mean square and the prescribed H ∞ performance constraint is satisfied. By constructing proper Lyapunov–Krasovskii functionals and employing stochastic analysis techniques, sufficient conditions are derived to ensure the existence of the desired estimator. Furthermore, the explicit expression of the gain of the desired estimator is described in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimator design approach.

Multi-almost periodicity in semi-discretizations of a general class of neural networks

In this paper, we present multi-almost periodicity of a general class of discrete-time neural networks derived from a well-known semi-discretization technique, that is, coexistence and exponential stability of 2N almost periodic sequence solutions of discrete-time neural networks subjected to external almost periodic stimuli. By using monotonicity and boundedness of activation functions, we construct 2N close regions to attain the existence of almost periodic sequence solutions. Meanwhile, some new and simple criteria are derived for the networks to converge exponentially toward 2N almost periodic sequence solutions. As special cases, our results can extend to discrete-time analogues of periodic or autonomous neural networks and hence complement or improve corresponding existing ones. Finally, computer numerical simulations are performed to illustrate multi-almost periodicity of semi-discretizations of neural networks.

State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays

This paper is concerned with the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters and mixed time-delays. The parameters of the neural networks under consideration switch over time subject to a Markov chain. The networks involve both the discrete-time-varying delay and the mode-dependent distributed time-delay characterized by the upper and lower boundaries dependent on the Markov chain. By constructing novel Lyapunov-Krasovskii functionals, sufficient conditions are firstly established to guarantee the exponential stability in mean square for the addressed discrete-time neural networks with Markovian jumping parameters and mixed time-delays. Then, the state estimation problem is coped with for the same neural network where the goal is to design a desired state estimator such that the estimation error approaches zero exponentially in mean square. The derived conditions for both the stability and the existence of desired estimators are expressed in the form of matrix inequalities that can be solved by the semi-definite programme method. A numerical simulation example is exploited to demonstrate the usefulness of the main results obtained.

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.

Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays

In this paper, the stability analysis problem for a new class of discrete-time neural networks with randomly discrete and distributed time-varying delays has been investigated. Compared with the previous work, the distributed delay is assumed to be time-varying. Moreover, the effects of both variation range and probability distribution of mixed time-delays are taken into consideration in the proposed approach. The distributed time-varying delays and coupling term in complex networks are considered by introducing two Bernoulli stochastic variables. By using some novel analysis techniques and Lyapunov–Krasovskii function, some delay-distribution-dependent conditions are derived to ensure that the discrete-time complex network with randomly coupling term and distributed time-varying delay is synchronized in mean square. A numerical example is provided to demonstrate the effectiveness and the applicability of the proposed method.

Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays

In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained.

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov–Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.

Design of State Estimator for Discrete-Time Neural Networks: Delay-Independent Approach

In this Letter, the design problem of state estimator for a class of discrete-time neural networks is studied. A delay-independent linear matrix inequality (LMI) criterion for existence of the estimator is derived by using the Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example with simulation results is given to show the effectiveness of proposed method.

Stability and bifurcation of a class of discrete-time neural networks

In this paper, a class of discrete-time system modelling a network with two neurons is considered. Its linear stability is investigated and Neimark–Sacker bifurcation (also called Hopf bifurcation for map) is demonstrated by analyzing the corresponding characteristic equation. In particular, the explicit formula for determining the direction of Neimark–Sacker bifurcation and the stability of periodic solution is obtained by using the normal form method and the center manifold theory for discrete time system developed by Kuznetsov. The theoretical analysis is verified by numerical simulations.

Dynamics of a class of discrete-time neural networks and their continuous-time counterparts

The dynamical characteristics of continuous-time additive Hopfield-type neural networks are studied. Sufficient conditions are obtained for exponentially stable encoding of temporally uniform external stimuli. Discrete-time analogues of the corresponding continuous-time models are formulated and it is shown analytically that the dynamics of the networks are preserved by both continuous-time and discrete-time systems. Two major conclusions are drawn from this study: firstly, it demonstrates the suitability of the formulated discrete-time analogues as mathematical models for stable encoding of associative memories associated with external stimuli in discrete time, and secondly, it illustrates the suitability of our discrete-time analogues as numerical algorithms in simulating the continuous-time networks.

A NEW STOCHASTIC LEARNING ALGORITHM FOR NEURAL NETWORKS

A new stochastic learning algorithm using Gaussian white noise sequence, referred to as Subconscious Noise Reaction (SNR), is proposed for a class of discrete-time neural networks with time-dependent connection weights. Unlike the back-propagation-through-time (BTT) algorithm, SNR does not require the synchronous transmission of information backward along connection weights, while it uses only ubiquitous noise and local signals, which are correlated against a single performance functional, to achieve simple sequential (chronologically ordered) updating of connection weights. The algorithm is derived and analyzed on the basis of a functional derivative formulation of the gradient descent method in conjunction with stochastic sensitivity analysis techniques using the variational approach.