Distributed Adaptive Containment Control for Coupled Reaction-Diffusion Neural Networks With Directed Topology

Finite-time H∞ output synchronization for DCRDNNs with multiple delayed and adaptive output couplings

This work concentrates on solving the finite-time H∞ output synchronization (FTHOS) issue of directed coupled reaction-diffusion neural networks (DCRDNNs) with multiple delayed and adaptive output couplings in the presence of external disturbances. Based on the output information, an adaptive law to adjust output coupling weights and a controller are respectively developed to ensure that the DCRDNNs achieve FTHOS. Then, in the special case of no external disturbances, a corollary on the finite-time output synchronization (FTOS) of the DCRDNNs with multiple delayed and adaptive output couplings is provided. In addition, a novel adaptive scheme to update output coupling weights is devised to ensure H∞ output synchronization (HOS) in the DCRDNNs with multiple delayed output couplings. Finally, the relevant simulation graphs are provided to certify the validity of several synchronization criteria.

Distributed adaptive robust containment control for reaction-diffusion neural networks with external disturbances under directed graphs

In this paper, the leader-follower robust synchronization issue is mainly addressed for reaction-diffusion neural networks (RDNNs) with multiple leaders and external disturbances under directed graphs. Based on the σ modification approach, we propose a novel distributed adaptive controller by adding a term [Formula: see text] to avoid the phenomenon of parameter drift, that is, the adaptive parameters grow to infinity. Meanwhile, different from the adaptive control algorithm proposed in the undirected graph, we introduce a new function χi(t) to provide additional freedom for the design to achieve robust containment when confronted with external disturbances. Further, the robustness of tracking synchronization with one leader is guaranteed by the proposed adaptive controller when the external disturbances concerning L2 norm are bounded. Finally, relevant numerical simulation graphics are displayed separately to verify the correctness of the related theoretical results.

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 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 OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.