Event-Triggered Synchronization Strategy for Multiple Neural Networks With Time Delay

Hybrid Adjusting Variables-Dependent Event-Based Finite-Time State Estimation for Two-Time-Scale Markov Jump Complex Networks

This article investigates the problem of dynamic event-triggered finite-time H∞ state estimation for a class of discrete-time nonlinear two-time-scale Markov jump complex networks. A hybrid adjusting variables-dependent dynamic event-triggered mechanism (DETM) is proposed to regulate the releases of measurement outputs of a node to a remote state estimator. Such a DETM contains both an additive dynamically adjusting variable (DAV) and a multiplicative adaptively adjusting variable. The aim is to design a DETM-based mode-dependent state estimator, which guarantees that the resultant error dynamics is stochastically finite-time bounded with H∞ performance. By constructing a mode-dependent Lyapunov function with multiple DAVs and a singular perturbation parameter associated with time scales, a matrix-inequalities-based sufficient condition is derived, the feasible solutions of which facilitate the design of the parameters of the state estimator. The validity of the designed state estimator and the superiority of the devised DETM are verified by two examples. It is verified that the devised DETM is capable of saving network resources and simultaneously improving the estimation performance.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Master-Slave Synchronization of Neural Networks With Unbounded Delays via Adaptive Method

Master-slave synchronization of two delayed neural networks with adaptive controller has been studied in recent years; however, the existing delays in network models are bounded or unbounded with some derivative constraints. For more general delay without these restrictions, how to design proper adaptive controller and prove rigorously the convergence of error system is still a challenging problem. This article gives a positive answer for this problem. By means of the stability result of unbounded delayed system and some analytical techniques, we prove that the traditional centralized adaptive algorithms can achieve global asymptotical synchronization even if the network delays are unbounded without any derivative constraints. To describe the convergence speed of the synchronization error, adaptive designs depending on a flexible ω -type function are also provided to control the synchronization error, which can lead exponential synchronization, polynomial synchronization, and logarithmically synchronization. Numerical examples on delayed neural networks and chaotic Ikeda-like oscillator are presented to verify the adaptive designs, and we find that in the case of unbounded delay, the intervention of ω -type function can promote the realization of synchronization but may destroy the convergence of control gain, and this however will not happen in the case of bounded delay.

A New Finite-Time Circadian Rhythms Learning Network for Solving Nonlinear and Nonconvex Optimization Problems With Periodic Noises

Nonlinear and nonconvex optimization problems are vital and fundamental problems in science and engineering fields. In this article, a novel finite-time circadian rhythms learning network (called FT-CRLN) is proposed for solving nonlinear and nonconvex optimization problems with periodic noises. Different from the traditional recurrent neural networks, the proposed FT-CRLN can suppress the periodic noise notably and achieve excellent convergence performance in solving nonlinear and nonconvex problems. The theoretical analysis and rigorous mathematical proof verify the superior convergence, high accuracy, and strong robustness of the proposed FT-CRLN. The simulation results demonstrate the effectiveness and robustness of the proposed FT-CRLN in solving nonlinear and nonconvex problems compared with other state-of-art neural networks.

Event-Based Synchronization for Multiple Neural Networks With Time Delay and Switching Disconnected Topology

This article discusses the synchronization problem for a class of multiple delayed neural networks (MDNNs) with a directed switching topology by using an event-triggering strategy. First, a new differential inequality with delay is shown, which is a generalization of Halanay-type inequalities. Then, the sufficient conditions of event-based synchronization (quasisynchronization) for MDNN with sequentially connected topology are obtained by using this inequality and the iterative method. Meantime, we prove that Zeno behavior can be avoided under the designed event-triggering rules. As an extension, MDNN with jointly connected topology is also discussed. Finally, a numerical example is listed to illustrate the results in theory analysis.

Distributed Heuristic Adaptive Neural Networks With Variance Reduction in Switching Graphs

This article proposes a distributed adaptive training method for neural networks in switching communication graphs to deal with the problems concerned with massive data or privacy-related data. First, the stochastic variance reduced gradient (SVRG) is used for the training of neural networks. Then, the authors propose a heuristic adaptive consensus algorithm for distributed training, which adaptively adjusts the weighted connectivity matrix based on the performance of each agent over the communication graph. Furthermore, it is proved that the proposed distributed heuristic adaptive neural networks ensure the convergence of all the agents to the optimum with a single communication among connected neighbors after every training step, which is also suitable for switching graphs. This theorem is verified by the simulation, which gives the results that fewer iterations are required for all agents to reach the optimum using the proposed heuristic adaptive consensus algorithm, and the SVRG can greatly decrease the fluctuations caused by the stochastic gradient and improve its performance with only a little extra computational cost.

A Unified Framework Design for Finite-Time and Fixed-Time Synchronization of Discontinuous Neural Networks

In this article, the problems of finite-time/fixed-time synchronization have been investigated for discontinuous neural networks in the unified framework. To achieve the finite-time/fixed-time synchronization, a novel unified integral sliding-mode manifold is introduced, and corresponding unified control strategies are provided; some criteria are established for selecting suitable parameters for solving the related issue, namely, the dynamics of neural network can reach the designed sliding-mode manifold in finite/fixed time, and stay on it thereafter. Moreover, the estimations of setting time are given out. The established unified framework can bring in various protocols by choosing the different parameters of controllers and sliding-mode manifold, which extend previous related results. Finally, some numerical examples are introduced to show the effectiveness and superiority of resulting conclusions.

Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control

This paper considers the drive-response synchronization of memristive neural networks (MNNs) with unknown parameters, where the unbounded discrete and bounded distributed time-varying delays are involved. Aiming at the unknown parameters of MNNs, the updating law of weight in response system and the gain of adaptive controller are proposed to realize the synchronization of delayed MNNs. In view of the limited communication and bandwidth, the event-triggered mechanism is introduced to adaptive control, which not only decreases the times of controller update and the amount of data sending out but also enables synchronization when parameters of MNNs are unknown. In addition, a relative threshold strategy, which is relative to fixed threshold strategy, is proposed to increase the inter-execution intervals and to improve the control effect. When the parameters of MNNs are known, the algebraic criteria of synchronization are established via event-triggered state feedback control by exploiting inequality techniques and calculus theorems. Finally, one simulation is presented to validate the effectiveness of the proposed results.