The Intermittent Control Of Successive Lag Synchronization On Networks With Noise Disturbance

Successive lag synchronization(SLS)is a new and important synchronization technology.SLS means that the nodes in the network are numbered in advance,and the latter node reaches the same state as the previous node after a certain time.SLS is very common in our life,such as the synchronous performance of aircraft formation,the sequential swimming of fish and so on.Although the control problem of SLS has been deeply studied in the past few years,the influence of noise disturbance on SLS is still unclear.Due to the low cost of the intermittent pinning control,this thesis focuses on the intermittent pinning control of SLS in complex dynamic networks with noise disturbance.Firstly,a distributed complex dynamic network model with noise disturbance is proposed.Previous studies on SLS either adopted centralized dynamic network model or didn’t consider the effect of noise.In the distributed linear coupling model with noise disturbance,the information of each node only depends on the information of its neighbors rather than all nodes,which has higher efficiency.Considering the influence of noise,it is more suitable for practical application.Secondly,in order to improve control efficiency and save economic cost,an intermittent pinning control strategy is designed.The strategy is activated only in the controlled interval and a small number of nodes.The sufficient conditions for the mean square stability of SLS are obtained by using the It(?) lemma,the Lyapunov function and the stability theory of stochastic differential equations.In accordance with these conditions,we can determine which nodes should be controlled or not.An interesting finding is that performing the control on at least half of each subinterval can ensure the stochastic stability of SLS.Further,the noise play a destructive role in SLS,and Chua’s circuit is used to verify the effectiveness of intermittent pinning control strategy.Finally,the network model is optimized.Considering that the coupling matrix of the above complex dynamic network model can only be the lower triangular matrix,it has strict requirements for the structure of the network.In order to solve the problem of SLS in general network topology structure,we further propose a new coupling strategy.By analyzing the stability conditions,it is found that the upper triangular part of the coupling matrix usually inhibits the network synchronization.When the coupling strength exceeds a certain threshold,the network will not synchronize,which is the biggest difference from the previous network models.Numerical experiments are carried out using Chua’s circuit to verify the effectiveness of the intermittent pinning strategy.