Adaptive Synchronization Of Complex Dynamical Networks With Unknown Topological Structure

In our daily life and intelligent networks,the complex dynamical networks have very wide application.Meanwhile,the synchronization of complex dynamical networks is a meaningful and interesting phenomenon.When investigating it,we mainly study the adaptive synchronization control problem of complex dynamical networks.In the process of researching the synchronization control of networks,there are two dynamical factors need to be considered: the one is the dynamical behavior of the nodes in the network,the other one is the connection between the connected nodes,which also can be called topological structure.According to the characteristics of the system with distributed time-varying delay and imprecise topological structure,based on the T-S fuzzy model,this paper mainly studies three kinds of synchronization control problems for complex dynamical networks:Firstly,this paper studies the synchronization problem of uncertain complex dynamical networks with distributed time-varying delay.In the existing research results,there are some papers study the synchronization of complex dynamical networks with constant distributed time-varying delay.However,in the case of unknown topological structure,the synchronization problem of networks with distributed time-varying delay is not solved.Therefore,this paper studies the synchronization control problem of unknown complex network with distributed time-varying delay.Based on the T-S fuzzy model,a new general class of complex network is proposed,and a new adaptive feedback controller is proposed.In this paper,the adaptive controller designed for each node is only related to the dynamical behavior of the nodes connected directly to the node.Based on Lyapunov stability theory,we obtain sufficient condition for the synchronization of fuzzy complex dynamical networks in linear matrix inequality(LMIs).The validity and correctness of the proposed theory is verified by the given numerical simulation.Secondly,the synchronization of unknown complex dynamical networks with differential coupling and distributed time-varying delay coupling is studied.Considering the dynamics of each node in the network may be different,and the state of the node is not only related with the general state of neighbor nodes,but also associated with the differential state of neighbor nodes,this paper considers the synchronization control problem of a more realistic complex dynamical network.In this paper,a new T-S fuzzy model is proposed to describe the unknown topological structure of complex networks.At the same time,different from the general Lyapunov function,this paper constructs a new type of fuzzy Lyapunov function.Compared with the general construction method,the proposed method has more higher design freedom.Finally,the conditions of asymptotic synchronization for complex network are given by designing a fuzzy adaptive feedback controller for the nodes in networks.The validity and correctness of the proposed theory is verified by the given numerical simulation.In the end,this paper studies the synchronization problem of the imprecise drive-response complex dynamical network with distributed time-varying delay.Based on the T-S fuzzy theory,a new T-S fuzzy model drive-response system is proposed to describe the unknown topological structure.In order to realize the synchronization between the fuzzy drive systems and fuzzy response systems,this paper designs fuzzy adaptive feedback controllers and adaptive parameter adaptive laws for the nodes in the response system.Finally,the linear matrix inequality(LMI)conditions for asymptotic synchronization and lag synchronization of complex dynamical networks are given.The validity and correctness of the proposed theory is verified by the given numerical simulations.At last,the development direction of the synchronization problem for unknown complex dynamical network is forecasted.