A Study Of Distributed Adaptive Synchronization Control Of Complex Dynamical Network

As the most important and basal problem of complex dynamical networks(CDNs), synchronization attracted much attention for a long time. On the one hand, there are large number of control method have been founded because of the complex structure and diversity of connection type. From the perspective of centralization, three kind of control method are mainly considered, they are: centralized control, decentralized control, and distributed control. Where distributed control is increasingly favored by scholars due to it combine with the information of neighbor nodes and state of located node, that is to say, this control method do not need the global information of whole network and it effectively utilize the connection characteristic of network. On the other hand, network with unknown coupling weights and distributed time delay are widely spread in nature and human society. How to synchronize above two kinds networks with distributed controller is a meaningful issue.This paper design adaptive controller use adaptive method and Lyapunov stability theory for complex dynamical networks. Details are as follows:Firstly, a new kind of distributed adaptive control approach is proposed for a class of complex dynamical network with both unknown time-varying coupling weights and unknown constant parameters, this controller use located dynamic and neighbor information at the same time. A new Lyapunov-Krasovskii function is built for stability analysis. The asymptotical synchronization can be achieved and estimations of parameters are bounded under proposed distributed adaptive control law. Finally, simulation example is provided to illustrate the feasibility of proposed control method.Secondly, a kind of complex dynamical networks with time-varying distributed time delay is studied by distributed adaptive control. Meanwhile, there are unknown time-varying coupling weights and unknown constant parameters in the system model. A new distributed control law is designed for above complex networks and system error converges to zero asymptotically under the proposed controller. Furthermore, to achieve faster synchronization, the Lyapunov-Krasovskii function and adaptive law are improved, the improved version ensure the exponential convergence of error system, the exponential decay rate can be get directly, and all the closed-loop signals are bounded in the sense of norm. Lastly, a simulation example is given to show the feasibility of the proposed controller.Third, Problem of topology identification with unknown control direction is discussed utilize Nussbaum function and La Salle’s invariance principle. Controller and adaptive law are designed to synchronize response system and driven system, and identify the topology of driven system. Lorenz system is used to verify the effectiveness of the proposed method.