Fast synchronization control and application for encryption-decryption of coupled neural networks with intermittent random disturbance

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Asynchronous State Estimation for Discrete-Time Switched Complex Networks With Communication Constraints

This paper is concerned with the asynchronous state estimation for a class of discrete-time switched complex networks with communication constraints. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the topology/coupling information. Also, the event-based communication, signal quantization, and the random packet dropout problems are studied due to the limited communication resource. With the help of switched system theory and by resorting to some stochastic system analysis method, a sufficient condition is proposed to guarantee the exponential stability of estimation error system in the mean-square sense and a prescribed performance level is also ensured. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem. Finally, the effectiveness of the proposed design approach is demonstrated by a simulation example.

Finite-Time State Estimation for Recurrent Delayed Neural Networks With Component-Based Event-Triggering Protocol

This paper deals with the event-based finite-time state estimation problem for a class of discrete-time stochastic neural networks with mixed discrete and distributed time delays. In order to mitigate the burden of data communication, a general component-based event-triggered transmission mechanism is proposed to determine whether the measurement output should be released to the estimator at certain time-point according to a specific triggering condition. A new concept of finite-time boundedness in the mean square is put forward to quantify the estimation performance by introducing a settling-like time function. The objective of the addressed problem is to construct an event-based state estimator to estimate the neuron states such that, in the presence of both mixed time delays and external noise disturbances, the dynamics of the estimation error is finite-time bounded in the mean square with a prescribed error upper bound. Sufficient conditions are established, via stochastic analysis techniques, to guarantee the desired estimation performance. By solving an optimization problem with some inequality constraints, the explicit expression of the estimator gain matrix is characterized to minimize the settling-like time. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design scheme.

Finite-Time Synchronization of Coupled Hierarchical Hybrid Neural Networks With Time-Varying Delays

This paper is concerned with the finite-time synchronization problem of coupled hierarchical hybrid delayed neural networks. This coupled hierarchical hybrid neural networks consist of a higher level switching and a lower level Markovian jumping. The time-varying delays are dependent on not only switching signal but also jumping mode. By using a less conservative weighted integral inequality and stochastic multiple Lyapunov-Krasovskii functional, new finite-time synchronization criteria are obtained, which makes the state trajectories be kept within the prescribed bound in a time interval. Finally, an example is proposed to demonstrate the effectiveness of the obtained results.

Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay

This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

Global Synchronization of Multiple Recurrent Neural Networks With Time Delays via Impulsive Interactions

In this paper, new results on the global synchronization of multiple recurrent neural networks (NNs) with time delays via impulsive interactions are presented. Impulsive interaction means that a number of NNs communicate with each other at impulse instants only, while they are independent at the remaining time. The communication topology among NNs is not required to be always connected and can switch ON and OFF at different impulse instants. By using the concept of sequential connectivity and the properties of stochastic matrices, a set of sufficient conditions depending on time delays is derived to ascertain global synchronization of multiple continuous-time recurrent NNs. In addition, a counterpart on the global synchronization of multiple discrete-time NNs is also discussed. Finally, two examples are presented to illustrate the results.

Synchronization of Arbitrarily Switched Boolean Networks

This paper investigates the complete synchronization problem for the drive-response switched Boolean networks (SBNs) under arbitrary switching signals, where the switching signals of the response SBN follow those generated by the drive SBN at each time instant. First, the definition of complete synchronization is introduced for the drive-response SBNs under arbitrary switching signals. Second, the concept of switching reachable set starting from a given initial state set is put forward. Based on it, a necessary and sufficient condition is derived for the complete synchronization of the drive-response SBNs. Last, we give a simple algebraic expression for the switching reachable set in a given number of time steps, and two computable algebraic criteria are obtained for the complete synchronization of the SBNs. A biological example is given to demonstrate the effectiveness of the obtained main results.

Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach

This paper considers the asymptotic and finite-time synchronization of drive-response memristive neural networks (MNNs) with time-varying delays. It is known that the parameters of MNNs are state-dependent, and hence the traditional robust control and analytical techniques cannot be directly applied. This difficulty is overcome by using the concept of Filippov solution. However, the special characteristics of MNNs may lead to unexpected parameter mismatch issue when different initial conditions are chosen. Based on a new robust control design, the mismatching issue is solved. Sufficient conditions are derived to guarantee the asymptotic synchronization of the considered MNNs with delays, which may be less conservative than synchronization criterion obtained by using existing methods. Moreover, without using the existing finite-time stability theorem, finite-time synchronization of the MNNs with delays is also investigated. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Integration-Enhanced Zhang Neural Network for Real-Time-Varying Matrix Inversion in the Presence of Various Kinds of Noises

Matrix inversion often arises in the fields of science and engineering. Many models for matrix inversion usually assume that the solving process is free of noises or that the denoising has been conducted before the computation. However, time is precious for the real-time-varying matrix inversion in practice, and any preprocessing for noise reduction may consume extra time, possibly violating the requirement of real-time computation. Therefore, a new model for time-varying matrix inversion that is able to handle simultaneously the noises is urgently needed. In this paper, an integration-enhanced Zhang neural network (IEZNN) model is first proposed and investigated for real-time-varying matrix inversion. Then, the conventional ZNN model and the gradient neural network model are presented and employed for comparison. In addition, theoretical analyses show that the proposed IEZNN model has the global exponential convergence property. Moreover, in the presence of various kinds of noises, the proposed IEZNN model is proven to have an improved performance. That is, the proposed IEZNN model converges to the theoretical solution of the time-varying matrix inversion problem no matter how large the matrix-form constant noise is, and the residual errors of the proposed IEZNN model can be arbitrarily small for time-varying noises and random noises. Finally, three illustrative simulation examples, including an application to the inverse kinematic motion planning of a robot manipulator, are provided and analyzed to substantiate the efficacy and superiority of the proposed IEZNN model for real-time-varying matrix inversion.

An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities

In this paper, the state estimation problem is investigated for a class of discrete-time complex networks subject to nonlinearities, mixed delays, and stochastic noises. A set of event-based state estimators is constructed so as to reduce unnecessary data transmissions in the communication channel. Compared with the traditional state estimator whose measurement signal is received under a periodic clock-driven rule, the event-based estimator only updates the measurement information from the sensors when the prespecified "event" is violated. Attention is focused on the analysis and design problem of the event-based estimators for the addressed discrete-time complex networks such that the estimation error is exponentially bounded in mean square. A combination of the stochastic analysis approach and Lyapunov theory is employed to obtain sufficient conditions for ensuring the existence of the desired estimators and the upper bound of the estimation error is also derived. By using the convex optimization technique, the gain parameters of the desired estimators are provided in an explicit form. Finally, a simulation example is used to demonstrate the effectiveness of the proposed estimation strategy.

Stochastic stability of delayed neural networks with local impulsive effects

In this paper, the stability problem is studied for a class of stochastic neural networks (NNs) with local impulsive effects. The impulsive effects considered can be not only nonidentical in different dimensions of the system state but also various at distinct impulsive instants. Hence, the impulses here can encompass several typical impulses in NNs. The aim of this paper is to derive stability criteria such that stochastic NNs with local impulsive effects are exponentially stable in mean square. By means of the mathematical induction method, several easy-to-check conditions are obtained to ensure the mean square stability of NNs. Three examples are given to show the effectiveness of the proposed stability criterion.

Global exponential synchronization of multiple memristive neural networks with time delay via nonlinear coupling

This paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays. A novel coupling scheme is introduced, in a general topological structure described by a directed or undirected graph, with a linear diffusive term and discontinuous sign term. Several criteria are derived based on the Lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme. Simulation results for several examples are given to substantiate the effectiveness of the theoretical results.

Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties

This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov-Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.

Zhang neural network for online solution of time-varying linear matrix inequality aided with an equality conversion

In this paper, for online solution of time-varying linear matrix inequality (LMI), such an LMI is first converted to a time-varying matrix equation by introducing a time-varying matrix, of which each element is greater than or equal to zero. Then, by employing Zhang et al.'s neural dynamic method, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online the converted time-varying matrix equation as well as the time-varying LMI. Such a ZNN model showed in an explicit dynamics exploits the time-derivative information of time-varying coefficients. In addition, theoretical analysis and results of the proposed ZNN model are discussed and presented to show its excellent performance on solving the time-varying LMI. Computer simulation results further demonstrate the efficacy of the proposed ZNN model for online solution of the time-varying LMI and the converted time-varying matrix equation.

Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays

This paper is concerned with the problems of exponential stability analysis and synchronization of discrete-time switched delayed neural networks. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with time-delays. Benefitting from the delay partitioning method and the free-weighting matrix technique, the conservatism of the obtained results is reduced. In addition, the decay estimates are explicitly given and the synchronization problem is solved. The results reported in this paper not only depend upon the delay, but also depend upon the partitioning, which aims at reducing the conservatism. Numerical examples are presented to demonstrate the usefulness of the derived theoretical results.

Coordination of multiagents interacting under independent position and velocity topologies

We consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. It is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions. Such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify. Rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory, matrix analysis as well as the Lyapunov stability theory.

Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects

This paper investigates the synchronization problem of coupled switched neural networks (SNNs) with mode-dependent impulsive effects and time delays. The main feature of mode-dependent impulsive effects is that impulsive effects can exist not only at the instants coinciding with mode switching but also at the instants when there is no system switching. The impulses considered here include those that suppress synchronization or enhance synchronization. Based on switching analysis techniques and the comparison principle, the exponential synchronization criteria are derived for coupled delayed SNNs with mode-dependent impulsive effects. Finally, simulations are provided to illustrate the effectiveness of the results.

New parameter-free simplified swarm optimization for artificial neural network training and its application in the prediction of time series

A new soft computing method called the parameter-free simplified swarm optimization (SSO)-based artificial neural network (ANN), or improved SSO for short, is proposed to adjust the weights in ANNs. The method is a modification of the SSO, and seeks to overcome some of the drawbacks of SSO. In the experiments, the iSSO is compared with five other famous soft computing methods, including the backpropagation algorithm, the genetic algorithm, the particle swarm optimization (PSO) algorithm, cooperative random learning PSO, and the SSO, and its performance is tested on five famous time-series benchmark data to adjust the weights of two ANN models (multilayer perceptron and single multiplicative neuron model). The experimental results demonstrate that iSSO is robust and more efficient than the other five algorithms.