The Research On Synchronization Of Complex Networks And Consensus Of Multi-Agent Systems Based On Adaptive Control Methods

In recent years, the complex networks have attracted more and more researchers from science and engineering fields. The research on synchronization problem of complex network has become one of the hot researches in control field, and it is one of strategic issues of science and technology in the 21st century. With the rapid development of distributed networks and multi-agent systems, consensus problem is the foundation of cooperation among multi-agents and one of the important directions of research on multi-agent systems and has been paid more and more attention by the researchers from different fields. Consensus problem becomes a new but important research subject in a group coordinated control field. Therefore, the research on synchronization problem of complex networks and consensus algorithm of multi-agent systems is very significant. This paper is devoted to the study of synchronization for evolving complex networks with unknown parameters and mismatch parameters, adaptive outer synchronization between two nonidentical networks using arbitrary coupling strength and the consensus of third-order multi-agent systems with perturbations. The research focuses mainly on the following several parts:1. Robust modified function projective synchronization in network with unknown parameters and mismatch parameters is investigated. We extended modified function projective synchronization (MFPS) from two systems to the network with unknown parameters and mismatch parameters. Based on Lyapunov stability theory, we designed suitable robust controllers and appropriate updated laws, such that MFPS in the driven-response complex network can be achieved. We performed numerical simulations to show that our scheme is effective.2. Adaptive outer synchronization between two nonidentical networks using arbitrary coupling strength is discussed. Based on Lyapunov stability theory, we prove that for networks with balanced structure topology, not only outer synchronization but also inner synchronization can be asymptotically reached by using arbitrary coupling strength. Then, the examples show that the coupling strength has great influence on the performance of outer synchronization for identical dynamical systems and nonidentical topology for a short time, but has little influence on the performance of outer synchronization for nonidentical dynamical systems and nonidentical topology. At last, we prove that this method can be also used for evolving complex networks.3. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have great influence on the convergence performance of errors for a short time.