Finite-Time Output Synchronization of Multiple Weighted Reaction–Diffusion Neural Networks With Adaptive Output Couplings

This article mainly considers the output synchronization (OS) problem of multiple weighted and adaptive output coupled reaction–diffusion neural networks (RDNNs) without and with coupling delays in finite time. Without coupling delays, an adaptive control law and an output feedback controller are, respectively, proposed to ensure that the multiple weighted and output coupled RDNNs are output synchronized and $H_{\infty }$ output synchronized in finite time. With coupling delays, an adaptive coupling weights control scheme and a novel feedback controller are put forward to make the multiple weighted RDNNs with output couplings achieve OS in finite time. Moreover, the finite-time $H_{\infty }$ OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and $H_{\infty }$ OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.

I. Introduction

For the past few years, coupled neural networks (NNs) have been extensively studied in diverse fields, such as brain neuroscience, biology, and chemistry [1], [2]. Synchronization is an interesting and significant dynamic behavior of coupled NNs, which has been investigated in depth, and a large number of crucial theoretical results have been acquired [3]–[8]. Coupled NNs can realize many dynamic characteristics through electronic circuits, but when electrons move in asymmetric electromagnetic fields [9]–[11], the diffusion effect is inevitable and the coupled reaction–diffusion neural network (RDNN) model is obtained. As research shows, the human brain has the ability to process information in parallel, which is similar to the synchronization of coupled RDNNs. In order to better simulate the function of the human brain and promote the progress of brain neuroscience, it is necessary to research the synchronization problem of coupled RDNNs and many important theoretical achievements have been gained in [12]–[16].