Study On Synchronization And Consensus For Complex Networks

The synchronization and consensus of complex networks is a hot research topic in the field of information engineering, biological engineering, artificial intelligence and pattern recognition. In recent years, the research on synchronization and consensus of complex networks has been widely concerned by domestic and foreign scholars. However, nonlinear dynamics, time delays of the signal transmission and the random uncertainty also effect the synchronization or consensus of the system. In order to study the evolution mechanism and changing trend of complex networks, we need to explore the synchronization and consensus of complex networks to control and utilize it. In this paper, we further study the problem of synchronization and consensus of complex networks. The main contents as follows:(1) We study the hybrid projective synchronization of Markovian jumping complex networks with mode-dependent time-varying delays. Firstly, for a given driving system, the response system connected by complex networks with nonlinear coupling is given, and the time-varying delays which are related to the mode are introduced. Then, the synchronization scheme is designed, by using the important inequality and linear matrix inequality (LMI) method, the conditions for achieving hybrid projection synchronization between the driving system and response system are derived.(2) The most results of the synchronization and consensus of complex network systems are based on linear system, there are also some literatures on the nonlinear uncertainty system, but there are not many literatures on the nonlinear system with event-triggered control. In this paper, we study the consensus of nonlinear multi-agent networks with event-triggered control. The consensus problem of nonlinear multi-agent networks with fixed topology and switching topology are analyzed, respectively. Further, this paper studies the synchronization problem of Markovian jumping complex networks with event-triggered control, and the Markovian jumping probability with partly unknown are also taken into account. Based on algebraic graph theory, stochastic differential equation theory and matrix theory in this paper, the sufficient conditions for achieving consensus of multi-agent networks and synchronizing the complex networks are obtained, respectively.(3) At present, the multi-agent networks are considered as dynamic models of the same order. Commonly, the dynamics of each agent are different in real systems. In order to solve the problem, this paper studies the consensus problem of heterogeneous multi-agent systems based on event-triggered control, the event-triggered control protocol is designed, by utilizing Lyapunov stability theory, the multi-agent systems with time-varying uncertain topology or not are studied, and the consensus conditions are given.In order to demonstrate the validity of the research results, we use the toolbox LMI of Matlab to obtain the feasible solution, the simulation results also show the effectiveness of the proposed theoretical results.