Distributed Adaptive Control for Synchronization in Directed Complex Networks

The dynamics of a complex network is generally very complicated due to the self-dynamics of the node and their interactions. Many existing conditions for reaching certain desirable dynamics in a complex network require global information of the network, for example, the spectrum of its Laplacian matrix. A challenging problem is how the network structure affects the network dynamics in a distributed way especially for directed networks, which is still unclear today. This paper investigates the impact of the network structure on a general directed complex network and develops a scheme to change the weights in a local manner to achieve a desired behavior. In particular, network synchronization is investigated, for which some distributed adaptive laws are designed on the coupling weights for reaching synchronization in a directed complex network. It is found that the directed spanning tree structure is helpful while the aggregation and circular structures are harmful for achieving network synchronization. It ...