Synchronization Analysis Of Dynamical Network Systems Based On Impulsive Effect

With the rapid development of network science,human society has entered a highly interconnected networked era.A dynamical network system consists of a large number of interconnected nodes which can represent various real-life individuals.The edges formed by these interconnected nodes characterize the interrelationships between individuals.Therefore,dynamical network systems have become powerful tools for describing the coupling relationship between various entities.Many practical problems can be effectively modeled using dynamical networks.Synchronization is one of the dynamical behaviors required for typical engineering applications of dynamical networks,making it a focal point of current theoretical and applied research.In practical applications,the state of the dynamical network systems can be subjected to impulsive effects caused by transient perturbation or sudden changes in the external environment(e.g.,system switching or human intervention).Impulsive effects can either promote the synchronization of the network system or lead to system performance degradation or even failure.Therefore,impulsive effects play a critical role in the synchronization analysis of network systems.However,the current theoretical research on impulsive effect still focuses on general impulsive control,and the impulse delay in the network is inevitable.Considering the impulsive control with delay in the design of impulsive controller can more accurately describe the practical problem.In addition,saving limited network resources,reducing control costs and resisting network attacks are also urgent problems to be solved in dynamical networks.This dissertation considers the actual environment,data transmission volume,control cost,and network security.The influence of impulsive control,impulsive perturbation,and impulse delay on the synchronization of neural network systems and complex network systems is analyzed using impulsive system theory,modern control theory,and Lyapunov stability theory.The primary research contents are as follows:1.A delayed impulsive controller that combines the event-triggered mechanism based on Lyapunov functional and forced time sequence is proposed to study the synchronization of coupled neural networks with internal network delay and impulse delay.This controller not only reduces resource consumption and control costs but also avoids situations where the event-triggered mechanism is not triggered for an extended period.Some synchronization criteria are established for coupled neural networks with different impulse delay sizes using the Lyapunov functional method,the comparison principle of discrete-time systems,and the iterative method.Additionally,sufficient conditions are obtained based on linear matrix inequalities to prevent Zeno behavior.Finally,two numerical examples are provided to illustrate the effectiveness of the theoretical results.2.The practical synchronization problem of delayed neural networks with external disturbances and parameter uncertainties is investigated.A new hybrid-triggered delayed impulsive control strategy is designed to reduce the control cost and ensure the synchronization performance.A switching law is established based on the relationship between the threshold function and the error trajectory of the drive-response systems to determine which triggering mechanism is activated.Furthermore,a comparison principle with impulse delay and external disturbance is proposed to explore the influence of impulse delay and external disturbance on system stability.Some practical synchronization criteria are established for the delayed neural network under the hybrid-triggered impulsive control scheme based on the proposed principle.Finally,two numerical examples are provided to demonstrate the validity and superiority of the theoretical results.3.To characterize a more realistic impulsive control method and consider the unavoidable delay in the sampling and transmission of impulsive information,a distribution delayed impulsive controller with stochastic impulsive gain is designed for directed coupled neural network systems.This design considers the state information between neighboring sub-networks and the fluctuation factor of impulsive gain,improving the adaptability and robustness of the control system.The influence of coupling delay and internal delay are also considered to construct a more general coupled neural network model.Using Lyapunov functional and mathematical analysis methods,almost surely synchronization criteria are established for directed coupled neural networks under the stochastic distribution delayed impulsive controller.Finally,numerical examples are provided to verify the robustness and superiority of the proposed stochastic gain control method.4.The synchronization control problem of multi-layer heterogeneous dynamical networks is studied via pinning impulsive control.First,a multi-layer dynamical network model under directed topology is established,which considers the heterogeneity of the intrinsic dynamics of each layer node and the effect of inter-layer coupling on communication delay.Then,from the perspective of impulsive control,an impulsive differential inequality with flexible impulse delay is proved by using the Razumikhin technique.Furthermore,synchronization criteria are established for multi-layer heterogeneous dynamical networks with time delay using the proposed inequality and obtain the convergence domain of synchronization error.Finally,for practical application,sufficient conditions are provided for quasi-synchronization of heterogeneous single-link robot arm networks and corresponding numerical examples to verify the effectiveness of the obtained results.5.The problem of almost surely synchronization of neural network systems with quality of service constraints is analyzed.Considering the complexity of the external network environment,malicious attacks during data transmission from sensor to controller and potential attacks from controller to actuator are modeled as nonlinear functions and impulsive perturbation sequences,respectively.The considered impulsive instants and impulsive gains are all random due to the randomness of network attacks.Almost surely synchronization criteria are established under random attack signals based on the BorelCantelli lemma and stochastic system theory.Finally,a numerical example is provided to demonstrate the feasibility and superiority of the theoretical results.