Distributed Event-triggered Synchronization For Generally Uncertain Random Networks

During the last two decades,the study of nonlinear network has received much research attention due to its suitability in describing the mutual interaction of states in many real systems,such as disease transmission?computer viruses spreading?social behaviors?smart grid system?internet communication.Recently,scholars have been working on different types of complex networks,including Markov switched networks,directed networks,nonlinear delay networks,random networks,and so on.Complex networks are often disturbed by random environments,so researchers have begun to pay attention to the synchronization of complex networks in random environments.In order to achieve synchronization of random networks,it is necessary to design a reasonable control strategy.This thesis adopts a distributed event excitation sampling strategy,which does not require continuous control during the control process,and triggers control only when necessary,and the excitation frequency will be lower.This thesis aims to investigate the synchronization issue for the random networks with generally uncertain transition rates via event-triggered sampling strategy.The main contents include the following aspects:Firstly,the significance of the research background of complex networks and the main work and innovations of this paper are explained.Secondly,the synchronization problem for pull-based distributed event-triggered control for nonlinear directed networks with uncertain transition rates and delay is studied.In this network model,a generalized uncertain Markov chain is introduced.The generalized uncertain transition rates are reflected in two aspects: 1)Some elements of the transition matrix are completely unknown;2)The estimated values of some elements of the transition matrix are known.A pull-based distributed event-based sampling control strategy is designed.By constructing a suitable Lyapunov function,the sufficient conditions for exponential synchronization are derived using Halanay's inequality theory.Finally,this chapter calculates the lower bound of the time interval of this distributed event-triggered sampling strategy to avoid Zeno phenomenon.Numerical simulation with Matlab is used to confirm the validity ofthe theoretical results.Then,the issue of achieving asymptotically exponential synchronization in mean square for push-based directed random network is discussed through distributed event-triggered control.In real life,noise is often inevitable.Therefore,this chapter introduces Brownian motion to simulate noise during signal transmission.A distributed event-triggered sampling strategy to avoid Zeno phenomenon is designed.By using Lyapunov stability theory and related random process knowledge,the sufficient conditions for the network model to achieve asymptotically exponential synchronization in mean square are obtained.A network model is given as a numerical example to verify the correctness of the theoretical results.Finally,under a distributed event-triggered sampling strategy,the almost sure synchronization problem of directed complex networks without strong connectedness is considered.This chapter introduces a hierarchical approach to collapse each strongly connected component into a single vertex,then the large-scale network becomes a condensed digraph.A stochastic Lyapunov-Krasovskii function is designed.Under distributed event-triggered sampling strategy,the sufficient conditions for almost sure synchronization of a non-strongly connected network are derived utilizing Lyapunov stability theory and the theory of asymptotically autonomous systems.In numerical simulation,this chapter gives an example of the model,and the simulation results obtained confirm that the synchronization conditions are sufficiently effective.