Pinning Control for Complete Synchronization of Complex Dynamical Networks

This chapter first introduces some complex network models and then gives both local and global stability conditions for complete synchronization of complex dynamical networks. In addition, the concept of virtual control of pinned complex dynamical networks is introduced to illustrate the principle of pinning control. The main reason is explained for why significantly less local controllers are required by specifically pinning the most highly connected nodes in a scale-free network than those required by the randomly pinning scheme, and why there is no significant difference between specifically and randomly pinning schemes for controlling random dynamical networks. Finally, a novel pinning scheme based on ControlRank (CR) is introduced, which is a vertex centrality index exploring the link structure of the directed networks. Moreover, it is shown that pinning the vertex with largest CR is much more effective than pinning the vertex with largest out-degree.