Abstract
This paper investigates the pinning synchronization analysis of linearly coupled reaction-diffusion neural networks (RDNNs) with unknown time-varying coupling strengths and unknown time-varying delay. By constructing a Lyapunov-Krasovskii-like composite energy functional (CEF) and applying the well-known LaSalle’s invariance principle, an adaptive learning control is designed to guarantee the asymptotic convergence of the synchronization error, several sufficient conditions of the synchronization are derived. Compared with the existing results, the update laws do not need the information of the characteristics of the identical node and the coupling matrices. An example shows the proposed theoretical result is feasible and effective.
Highlights
In the past few decades, neural networks (NNs) have become a hot topic due to their wide and important applications, such as signal transmission, image processing, machine learning, and pattern recognition, and so on
In reference [ ], based on the linear matrix inequality (LMI) method, two delay-dependent criteria were derived to ensure the exponential stability of the error systems, which implied the master systems to synchronize with the slave systems
Compared with the previous works, the main contributions of this paper lie in the following. ( ) We extend the existing concept of composite energy functional (CEF) to the time-delay setting, and a class of linearly coupled reaction-diffusion neural networks (RDNNs) with time-varying parameters and time-varying delays are given under the assumption that all time-varying parameters have a common periodicity
Summary
In the past few decades, neural networks (NNs) have become a hot topic due to their wide and important applications, such as signal transmission, image processing, machine learning, and pattern recognition, and so on. Based on the Lyapunov stability theory and Halanay inequality, by virtue of drive-response concept and time-delay feedback control techniques, reference [ ] proposed several sufficient conditions for the exponential synchronization of two identical chaotic delayed NNs with stochastic perturbation. In reference [ ], based on the linear matrix inequality (LMI) method, two delay-dependent criteria were derived to ensure the exponential stability of the error systems, which implied the master systems to synchronize with the slave systems. The non-fragile controller can be obtained by solving a set of LMIs. In reference [ ], by introducing an improved Lyapunov-Krasovskii functional and employing convex combination approach, a delaydependent output feedback controller was derived to achieve synchronization with the help of a master-slave concept and linear matrix inequality approach
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