Adaptive Exponential Synchronization of Multislave Time-Delayed Recurrent Neural Networks With Lévy Noise and Regime Switching

Distributed Adaptive Optimization Algorithm for High-Order Nonlinear Multi-Agent Stochastic Systems with Lévy Noise

An adaptive neural network output-feedback control strategy is proposed in this paper for the distributed optimization problem (DOP) of high-order nonlinear stochastic multi-agent systems (MASs) driven by Lévy noise. On the basis of the penalty-function method, the consensus constraint is removed and the global objective function (GOF) is reconstructed. The stability of the system is analyzed by combining the generalized Itô's formula with the Lyapunov function method. Moreover, the command filtering mechanism is introduced to solve the "complexity explosion" problem in the process of designing virtual controller, and the filter errors are compensated by introducing compensating signals. The proposed algorithm has been proved that the outputs of all agents converge to the optimal solution of the DOP with bounded errors. The simulation results demonstrate the effectiveness of the proposed approach.

Bounded Antisynchronization of Multiple Neural Networks via Multilevel Hybrid Control

The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Synchronization for stochastic coupled networks with Lévy noise via event-triggered control

This paper addresses the realization of almost sure synchronization problem for a new array of stochastic networks associated with delay and Lévy noise via event-triggered control. The coupling structure of the network is governed by a continuous-time homogeneous Markov chain. The nodes in the networks communicate with each other and update their information only at discrete-time instants so that the network workload can be minimized. Under the framework of stochastic process including Markov chain and Lévy process, and the convergence theorem of non-negative semi-martingales, we show that the Markovian coupled networks can achieve the almost sure synchronization by event-triggered control methodology. The results are further extended to the directed topology, where the coupling structure can be asymmetric. Furthermore, we also proved that the Zeno behavior can be excluded under our proposed approach, indicating that our framework is practically feasible. Numerical simulations are provided to demonstrate the effectiveness of the obtained theoretical results.

Stochastic analysis of COVID-19 by a SEIR model with Lévy noise

We propose a Lévy noise-driven susceptible-exposed-infected-recovered model incorporating media coverage to analyze the outbreak of COVID-19. We conduct a theoretical analysis of the stochastic model by the suitable Lyapunov function, including the existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium; we deduce a stochastic basic reproduction number R₀ ^s for the extinction of disease, that is, if R₀ ^s≤1, the disease will go to extinction. Particularly, we fit the data from Brazil to predict the trend of the epidemic. Our main findings include the following: (i) stochastic perturbation may affect the dynamic behavior of the disease, and larger noise will be more beneficial to control its spread; (ii) strengthening social isolation, increasing the cure rate and media coverage can effectively control the spread of disease. Our results support the feasible ways of containing the outbreak of the epidemic.

Deep Hyperspectral Image Sharpening

Hyperspectral image (HSI) sharpening, which aims at fusing an observable low spatial resolution (LR) HSI (LR-HSI) with a high spatial resolution (HR) multispectral image (HR-MSI) of the same scene to acquire an HR-HSI, has recently attracted much attention. Most of the recent HSI sharpening approaches are based on image priors modeling, which are usually sensitive to the parameters selection and time-consuming. This paper presents a deep HSI sharpening method (named DHSIS) for the fusion of an LR-HSI with an HR-MSI, which directly learns the image priors via deep convolutional neural network-based residual learning. The DHSIS method incorporates the learned deep priors into the LR-HSI and HR-MSI fusion framework. Specifically, we first initialize the HR-HSI from the fusion framework via solving a Sylvester equation. Then, we map the initialized HR-HSI to the reference HR-HSI via deep residual learning to learn the image priors. Finally, the learned image priors are returned to the fusion framework to reconstruct the final HR-HSI. Experimental results demonstrate the superiority of the DHSIS approach over existing state-of-the-art HSI sharpening approaches in terms of reconstruction accuracy and running time.