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.