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

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.

Finite-Time Consensus Adaptive Neural Network Control for Nonlinear Multiagent Systems Under PDE Models

In this article, a novel adaptive control method based on neural networks is proposed for a class of multiagent systems (MASs) with nonlinear functions and external disturbances. First, the approximation properties of neural networks are used to approximate the MAS partial differential equation (PDE) model with nonlinear terms containing two variables, time ${t}$ , and spatial variable ${x}$ . Second, an adaptive controller is constructed to actuate the parabolic MAS to reach consensus under external disturbances. Based on this, the finite-time theorem and special inequalities are applied to prove the stability of the closed-loop system. Thus, MAS that have nonlinear functions and external disturbances are enabled with finite-time consensus. Finally, the effectiveness of the proposed control method is demonstrated by numerical simulations.

Adaptive Drive-Response Synchronization of Timescale-Type Neural Networks With Unbounded Time-Varying Delays

In recent years, adaptive drive-response synchronization (DRS) of two continuous-time delayed neural networks (NNs) has been investigated extensively. For two timescale-type NNs (TNNs), how to develop adaptive synchronization control schemes and demonstrate rigorously is still an open problem. This article concentrates on adaptive control design for synchronization of TNNs with unbounded time-varying delays. First, timescale-type Barbalat lemma and novel timescale-type inequality techniques are first proposed, which provides us practical methods to investigate timescale-type nonlinear systems. Second, using timescale-type calculus, novel timescale-type inequality, and timescale-type Barbalat lemma, we demonstrate that global asymptotic synchronization can be achieved via adaptive control under algebraic and matrix inequality criteria even if the time-varying delays are unbounded and nondifferentiable. Adaptive DRS is discussed for TNNs, which implies our control schemes are suitable for continuous-time NNs, their discrete-time counterparts, and any combination of them. Finally, numerical examples on TNNs and timescale-type chaotic Ikeda-like oscillator with unbounded time-varying delays are carried out to verify the adaptive control schemes.