Wanli Zhang

Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations

This paper concerns the problem of finite-time synchronization for a class of complex-valued neural networks (CVNNs) with both time-varying and infinite-time distributed delays (mixed delays). Both the driving and response CVNNs are disturbed by external uncertain perturbations, which may be nonidentical. A simple state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time. By using inequality techniques and constructing some new Lyapunov–Krasovskii functionals, several sufficient conditions are derived to ensure the synchronization. It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinite-time distributed delays, while it can be explicitly estimated for the CVNNs with bounded delays. The settling time is dependent on both the delays and the initial value of the error system. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

Fixed-time stabilization of impulsive Cohen–Grossberg BAM neural networks

This article is concerned with the fixed-time stabilization for impulsive Cohen-Grossberg BAM neural networks via two different controllers. By using a novel constructive approach based on some comparison techniques for differential inequalities, an improvement theorem of fixed-time stability for impulsive dynamical systems is established. In addition, based on the fixed-time stability theorem of impulsive dynamical systems, two different control protocols are designed to ensure the fixed-time stabilization of impulsive Cohen-Grossberg BAM neural networks, which include and extend the earlier works. Finally, two simulations examples are provided to illustrate the validity of the proposed theoretical results.

Fixed-time consensus of complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties

Abstract In this paper, the fixed-time consensus problem for complex dynamical networks with nonlinear coupling and fuzzy state-dependent uncertainties is discussed. Different from most existing publications, the controller is designed as a fuzzy logic system, which is applicable for complex dynamical networks with system uncertainties and unknown topology to ensure the fixed-time consensus. Furthermore, compared with the initial-condition based finite-time consensus, the settling time is bounded by a constant within fixed-time regardless of the initial condition. Based on the Lyapunov stability theory and inequality techniques, some sufficient criteria for fixed-time consensus are obtained. Finally, two numerical examples are granted to display the performance of the obtained results.

Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control

This paper focuses on stochastic exponential synchronization of delayed memristive neural networks (MNNs) by the aid of systems with interval parameters which are established by using the concept of Filippov solution. New intermittent controller and adaptive controller with logarithmic quantization are structured to deal with the difficulties induced by time-varying delays, interval parameters as well as stochastic perturbations, simultaneously. Moreover, not only control cost can be reduced but also communication channels and bandwidth are saved by using these controllers. Based on novel Lyapunov functions and new analytical methods, several synchronization criteria are established to realize the exponential synchronization of MNNs with stochastic perturbations via intermittent control and adaptive control with or without logarithmic quantization. Finally, numerical simulations are offered to substantiate our theoretical results.

Global asymptotical stability for a class of non-autonomous impulsive inertial neural networks with unbounded time-varying delay

This article is concerned with the global asymptotical stability of non-autonomous impulsive inertial neural networks with unbounded delay. A new impulsive differential delay inequality which involves unbounded and non-differential delay is established. Moreover, based on a new impulsive differential delay inequality, new analysis techniques can effectively avoid the difficulties caused by unbounded delay and impulses, and several novel delay-dependent inequalities are obtained to ensure the global stability of this model. In the end, three examples are given to claim the validity of theoretical analysis.

Finite-time synchronization of complex networks with non-identical nodes and impulsive disturbances

This paper investigates the finite-time synchronization of complex networks (CNs) with non-identical nodes and impulsive disturbances. By utilizing stability theories, new 1-norm-based analytical techniques and suitable comparison, systems, several sufficient conditions are obtained to realize the synchronization goal in finite time. State feedback controllers with and without the sign function are designed. Results show that the controllers with sign function can reduce the conservativeness of control gains and the controllers without sign function can overcome the chattering phenomenon. Numerical simulations are offered to verify the effectiveness of the theoretical analysis.