Cluster Synchronization Control And State Estimation For Several Classes Of Switched Complex Dynamical Networks

Currently,complex networks with complicated structure are ubiquitous,such as,the Internet,transportation networks,power grids,social networks,neural networks.As one of the hot research topics in the natural field,complex dynamical networks have a wide range of applications in various fields,such as,economics,biology,engineering.Synchronization is one of the typical behaviors in the network.The synchronization issue of complex dynamical networks has naturally attracted a lot of attention from scholars,and obtained fruitful results.At present,the research object of complex dynamical networks is mainly the static network,that is,the topology of the network and the coupling weight are fixed.However,in many real networks,due to the aging of components,changes in the external environment,and other factors in the actual systems,the coupling forms and the topology structure will change,which means that it is not accu-rate to use a single system to simulate the node characteristics in the network.Thus,the idea of switched systems is introduced into the complex dynamical net-work and it's very meaningful to study the dynamical behaviors of the switched complex dynamical networks.In addition,not all complete synchronization is beneficial to human beings,and cluster synchronization is an extremely impor-tant synchronization form,which is a common nonlinear phenomenon in nature.Therefore,it's vital of researching the internal properties of cluster synchroniza-tion in theoretical,and exploring effective analysis methods to investigate cluster synchronization problems with switched complex dynamical networks is very im-portant in both theoretical and application.In this paper,by applying the generalized Ito formula,Lyapunov function method,stability theory of dynamical systems,and so on,the stability issue of a class of switched system with high and low frequency switching signals is analyzed,and some criteria ensuring the system to be global mean square ex-ponential stability and stabilization are derived.Besides,this paper focuses on the cluster synchronization issues of complex dynamical networks with switch-ing.Via pinning control strategy,dynamic event-triggered mechanism,linear matrix inequalities,theory of switching systems,graph theory,etc,the switch-ing laws and controller gains of the networks are designed to ensure that such networks perform asymptotic/finite-time/prescribed-time cluster synchroniza-tion.Moreover,the conditions to guarantee the finite-time boundedness of state estimation errors are established by using the non-periodic sampling strategy,event-triggered mechanism,stochastic differential equation theory,etc.This pa-per enriches the stability theory of switched systems and the synchronization control theory of complex dynamical networks,which can solve some key prob-lems such as cluster synchronization control of complex dynamical networks with switching signals.The main research contents and innovations of this paper are as follows:(1)This paper emphasizes the stability and stabilization issue of a class of switched systems with flexible switching signals and Levy noise.By apply-ing theory of switched system and the mathematical induction,some sufficient conditions ensuring the global means square exponential stability and stabiliza-tion of uncertain switched delay systems are derived.Different from dwell-time and average dwell-time methods,the switching law with high-frequency and low-frequency switching signals depends on the partial dwell time.Based on the partial dwell-time method,even there is some high-frequency switching in some time intervals,the system is mean square exponentially stable as long as the partial dwell time satisfies certain conditions.(2)A class of complex dynamic networks with constrained switching signals are established in this paper.We investigate the cluster synchronization control issues of such networks based on the dynamic event-triggered scheme.Compared with the static event-triggered mechanism,the fact that the introduction of the dynamic event-triggered mechanism can further save network communication resources has been provided.By constructing piecewise continuous Lyapunov functions and utilizing some mathematical analysis techniques,the appropriate pinning controllers are designed and the cluster synchronization conditions are proposed.The results obtained can be further extended to more general switched complex dynamical networks.(3)Considering the fact that the matched controller and the switched com-plex dynamical networks cannot be switched at the same time,this paper focuses on the finite-time cluster synchronization problems of switched complex dynami-cal networks with multi-proportional delays and asynchronous switching.By ap-plying the average dwell-time method and parameters changing,some criteria are developed to guarantee that the networks are finite-time cluster synchronization.Moreover,some conditions ensuring the switched systems to be prescribed-time stable are derived,which can be extended to more general switched systems.The results derived enrich the synchronization control theory of complex dynamical networks with proportional delays.(4)For the requirement that tasks must be completed within a certain time in the actual control system,the prescribed-time cluster synchronization prob-lem of uncertain switched complex dynamical networks is explored.Combining matrix decomposition and multiple Lyapunov functions method,conditions have been established to ensure that such networks can achieve the desired perfor-mance in finite time which is given in advance.Moreover,sufficient conditions ensuring the switched systems to be prescribed-time stable are derived,which can be extended to prescribed-time control issues of general systems.(5)This paper investigates the state estimation issues for a class of complex dynamical networks.A concept of finite-time boundedness in mean square and pth moment is proposed to design the appropriate state estimators for a class of delayed complex dynamical networks with random parameters.Furthermore,an aperiodic sampled-data event-triggered mechanism is introduced to study the finite-time boundedness state estimation issues.The finite-time boundedness conditions are obtained based on the stochastic differential equation analysis techniques and the stability theory of dynamical systems.The results obtained can be extended to switched complex dynamical networks.