Master-Slave Synchronization of Delayed Neural Networks With Time-Varying Control

Variable Gain Impulsive Synchronization for Discrete-Time Delayed Neural Networks and Its Application in Digital Secure Communication

This article revisits the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs) in the presence of disturbance in the input channel. A new Lyapunov approach based on double Lyapunov functionals is introduced for analyzing exponential input-to-state stability (EISS) of discrete impulsive delayed systems. In the framework of double Lyapunov functionals, a pair of timer-dependent Lyapunov functionals are constructed for impulsive DDNNs. The pair of Lyapunov functionals can introduce more degrees of freedom that not only can be exploited to reduce the conservatism of the previous methods, but also make it possible to design variable gain impulsive controllers. New design criteria for impulsive stabilization and impulsive synchronization are derived in terms of linear matrix inequalities. Numerical results show that compared with the constant gain design technique, the proposed variable gain design technique can accept larger impulse intervals and equip the impulsive controllers with a stronger disturbance attenuation ability. Applications to digital signal encryption and image encryption are provided which validate the effectiveness of the theoretical results.

Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

Event-based fixed-time synchronization of neural networks under DoS attack and its applications

In this paper, the fixed-time synchronization control for neural networks with discontinuous data communication is investigated. Due to the transmission blocking caused by DoS attack, it is intractable to establish a monotonically decreasing Lyapunov function like the conventional analysis of fixed-time stability. Therefore, by virtue of recursive and reduction to absurdity approaches, novel fixed-time stability criteria where the estimated upper bound of settling-time is inherently different from existing results are presented. Then, based on the developed conditions, an event-triggered control scheme that can avoid Zeno behavior is designed to achieve synchronization of master-slave neural networks under DoS attack within a prescribed time. For comparison, the established control scheme is further discussed under the case without DoS attack, and the circumstance that there is no attack or event-triggered mechanism, respectively. Simulation results are finally provided to illustrate the significant and validity of our theoretical research. Especially, in terms of encryption and decryption keys generated from the synchronization behavior of chaotic networks, we specifically discuss the application of the proposed fixed-time synchronization scheme to image and audio encryption.

H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control

This paper investigates the H∞ master-slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov-Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.

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.

Bounded synchronization for uncertain master-slave neural networks: An adaptive impulsive control approach

This paper investigates the bounded synchronization of the discrete-time master-slave neural networks (MSNNs) with uncertainty. To deal with the unknown parameter in the MSNNs, a parameter adaptive law combined with the impulsive mechanism is proposed to improve the estimation efficiency. Meanwhile, the impulsive method also is applied to the controller design for saving the energy. In addition, a novel time-varying Lyapunov functional candidate is employed to depict the impulsive dynamical characteristic of the MSNNs, wherein a convex function related to the impulsive interval is used to obtain a sufficient condition for bounded synchronization of the MSNNs. Based on the above condition, the controller gain is calculated utilizing an unitary matrix. An algorithm is proposed to reduce the boundary of the synchronization error by optimizing its parameters. Finally, a numerical example is provided to illustrate the correctness and the superiority of the developed results.

State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays

In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.