| Synchronization is one of the most common group behaviors in complex network systems.Considering that network synchronization has far-reaching significance for revealing many phenomena in nature and analyzing the mechanism of neuronal networks,thus synchronization of complex network systems has received extensive attention from scholars in various fields.In addition,time delay is a common phenomenon in nature and human society.Generally speaking,there are two types of time delays in network systems: internal delay and couple delay.In view of the advantages of intermittent control in reducing control costs and being implemented conveniently in practical applications,this thesis aims to explore global synchronization problems for two classes of directed network systems with mixed delays via nonperiodic intermittent control.The main research contents involve the following two aspects.Firstly,global synchronization problem for a class of complex directed network systems with internal delay and distributed-delay coupling is analyzed via nonperiodic intermittent control.Based on the reduction to absurdity and mathematical induction method,some sufficient conditions to guarantee global synchronization of the addressed delayed directed network systems are derived analytically.Different from the existing works,the control type here is nonperiodic intermittent with changeable control periods,which expands the scope of practical application of intermittent control scheme.Finally,a numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.Then,under intermittent control scheme,pinning synchronization of a class of complex directed network systems with hybrid coupling is investigated,in which hybrid coupling is composed of constant coupling,discrete-delay coupling and distributed-delay coupling.By combining the pinning scheme with the nonperiodic intermittent control technology,some criteria are established to ensure global synchronization of the delayed network systems under study.Furthermore,to decrease the intermittent feedback control gains,an adaptive intermittent pinning controlapproach is developed and the validity of this method is also rigorously proved through constructing a piecewise continuous Lyapunov function.Additionally,an effective pinned-nodes selection strategy is also provided to determine what kind of nodes should be picked to be controlled.Numerical examples are finally given to illustrate the effectiveness of the proposed control methodology. |
