Abstract
This paper investigates the robust adaptive exponential synchronization in mean square of stochastic perturbed chaotic delayed neural networks with nonidentical parametric uncertainties. A robust adaptive feedback controller is proposed based on Gronwally’s inequality, drive-response concept, and adaptive feedback control technique with the update laws of nonidentical parametric uncertainties as well as linear matrix inequality (LMI) approach. The sufficient conditions for robust adaptive exponential synchronization in mean square of uncoupled uncertain stochastic chaotic delayed neural networks are derived in terms of linear matrix inequalities (LMIs). The effect of nonidentical uncertain parameter uncertainties is suppressed by the designed robust adaptive feedback controller rapidly. A numerical example is provided to validate the effectiveness of the proposed method.
Highlights
Synchronization of chaotic delayed neural networks has been an intensive topic because of its promising connections with many disciplines, such as image encryption [1], image processing [2], harmonic oscillation generation [3], and secure communications [4,5,6]
This paper investigates the robust adaptive exponential synchronization in mean square of stochastic perturbed chaotic delayed neural networks with nonidentical parametric uncertainties
The authors in [29] were concerned with the problem of exponential synchronization for stochastic jumping chaotic neural networks (SJCNNs) with mixed delays and sector nonlinearities by employed Lyapunov-Krasovskii functional and free-weighting matrix method and proposed a delay-dependent feedback controller with sector nonlinearities to achieve the synchronization in mean square in terms of linear matrix inequalities (LMIs)
Summary
Synchronization of chaotic delayed neural networks has been an intensive topic because of its promising connections with many disciplines, such as image encryption [1], image processing [2], harmonic oscillation generation [3], and secure communications [4,5,6]. According to the best of our knowledge, there are still few results about the synchronization of stochastic perturbed chaotic delayed neural networks with nonidentical parametric uncertainties. The main aim is to design a robust adaptive feedback controller with the update laws of nonidentical parametric uncertainties and find some sufficient conditions in order to guarantee exponential synchronization in mean square for uncoupled chaotic delayed neural networks with stochastic perturbation and parametric uncertainties. Based on Gronwally’s inequality, drive-response concept, adaptive feedback control technique, and linear matrix inequality (LMI) approach, several sufficient conditions in the form of linear matrix inequalities (LMIs) are derived to ensure exponential synchronization in mean square for uncoupled uncertain stochastic chaotic delayed neural networks. The notation ⋆ always denotes the symmetric block in one symmetric matrix
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