Research On Control Of Two Kinds Of Group Behaviors In Fractional-Order Network Systems

Complex network systems,as an effective way to describe complex systems in the real world,have attracted the attention and research of many scholars both at home and abroad.Currently,most of the research works about complex network systems focus on integer-order network systems.Nevertheless,many real-world systems usually are fractional-order systems.Therefore,fractional-order network systems can better reveal the characteristics of real complex systems.As an significant group behavior,synchronization is the important research area of dynamics of complex network systems.In recent years,the investigation of synchronization in fractional-order network systems has made some progress,while the problems of quasi-synchronization and cluster synchronization have been rarely studied.In view of this,this thesis mainly discusses the quasi-synchronization problem of fractional-order heterogeneous network systems and the finite-time cluster synchronization one of fractional-order directed network systems with community structure,the main research contents include the following two aspects:(1)Based on an aperiodic intermittent pinning control scheme,the problem of quasi-synchronization for fractional-order heterogeneous network systems is addressed.According to the properties of the Mittag-Leffler function,a new fractional differential inequality is first obtained.Then,by applying aperiodic intermittent controllers to partial network nodes,some sufficient conditions for global quasi-synchronization of the network systems under study are derived with the help of the established new fractional inequality and Lyapunov function method.Moreover,the estimations of exponential convergence rate and error bound of the quasi-synchronization are also given.Finally,an numerical example is provided to verify the correctness of our theoretical analysis.(2)By using an adaptive control approach,the finite-time cluster synchronization problem of fractional-order directed network systems with community structure is considered.Through designing a hybrid adaptive controller and employing some analysis techniques,a general sufficient condition is derived to ensure fractional-order directed network systems with community structure can achieve cluster synchronization within a finite time interval.In addition,based on the properties of the Mittag-Leffler function,the setting time for cluster synchronization is estimated,and it is found that the estimation value of of setting time is related to the fractional order of the network model and the parameters of the designed controller.Finally,numerical simulations are carried out to validate the effectiveness of the theoretical results.