Pinning Control Of Successive Lag Synchronization On Dynamical Networks With Noise Perturbation

In recent years,a new synchronization pattern has emerged: successive lag synchronization(SLS),that means two adjacent numbered nodes reach the same state with a time delay.Specifically,the SLS is defined in a single network,and it can be considered as a generalized form of LS,which is generally defined in coupled networks.The SLS may have many application scenarios.For example,in the formation control of multi-agent systems,the realization of SLS among agents’ spatial locations can keep their formation and avoid collision simultaneously.Although the SLS has been further investigated,there are few theoretical studies on SLS control for complex networks with noise perturbation.Therefore,this thesis investigates the pinning control of SLS on complex dynamical networks with noise perturbation.The main contents are as follows:A stochastic complex dynamical network with one-way connections is presented.The network structure has directional and weighted characteristics and the coupling matrix is a lower triangular matrix.Both the constant pinning control law and adaptive pinning control law are designed respectively to push the network to achieve the desired SLS.By utilizing the Lyapunov stability theory of stochastic differential equations,several sufficient conditions for the controlled networks to achieve the SLS are obtained.Meanwhile,the influences of network structure,noise strength and coupling strength on the realization of SLS are also discussed.We find that the number and position of pinned nodes can be determined definitely,and the noise suppresses the realization of SLS.Finally,all the theoretical results are verified by numerical simulations.In order to make the network model closer to reality,this thesis further proposes a new complex dynamical network with general structure and noise perturbation to realize the SLS.By introducing a new coupling strategy,the network structure can be arbitrary.In order to steer the SLS to desired states,both the constant and adaptive pinning control laws are designed.Then,several sufficient conditions guaranteeing the global stochastic asymptotical stability of SLS are derived by applying the Lyapunov stability theory of stochastic differential equations.Meanwhile,the connections from a node to the other nodes with smaller numbers will lead to the increase of pinned nodes.The results indicate that,for the both pinning control schemes,the coupling strength should belong to a bounded interval to make the SLS stable.The theoretical results are validated by Chua’s circuit.