Analysis and Control of Directed Complex Dynamical Networks

Society depends on a diversity of complex networks for its very existence. Important complex networks like the Internet and the power grid are becoming ever larger, encompassing up to hundreds of millions of nodes. They exhibit complex and often dynamic patterns of links between the nodes. Networks interact with one another, they are recursive and very often they are built on top of one another. Social networks, for example, are built upon information networks which are related to communication networks which in turn are built on physical networks. This layered structure of interacting networks built on top of other networks is truly reflected in nature and society.In spite of society's profound dependence on networks, fundamental knowledge about them is primitive. Many physical networks, for example, global communication and transportation networks have quite advanced technological implementations, but their behavior under stress still cannot be predicted reliably. There is a great demand to study the realistic influences of network structure on its dynamical behavior.Fundamental knowledge are needed to predict the properties of large infrastructure networks. Analysis and control of very large networks is one of the major research challenges. Most of the research literature of complex dynamical networks is focused on the analysis of undirected network models, which provides only symmetrical information flow. However, the symmetrical model does not reflect the real circumstances, since the information flow between two connected nodes should be allowed to be shared differently. This means the corresponding graph has to be directed. Hence, this leads to a more realistic model, directed complex dynamical networks (DCDNs), to describe such complex networks.In this project, the researchers shall focus their attention on the dynamical analysis of DCDNs. Dynamics of such DCDNs (especially consensus and synchronization) will be analyzed by integrative and synthetical methodology under some practical constraints. The researchers shall verify some models to characterize the dynamical behavior of coupled systems. Algebraic connectivity-type concepts will be revealed for DCDNs by referring to spectral graph theory. Some control strategies will be designed to achieve the specified objectives, such as formation and tracking. The theoretical results generated in this project, if accomplished, will lay a solid foundation for the development of a wide range of fields, including cooperative control of unmanned vehicles or robots and pattern recognition.