Model reduction of network systems with structure preservation: Graph clustering and balanced truncation

A framework of complex networks can adequately describe a wide class of complex systems composing of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in the high complexity of a network system, which poses intense challenges to system management and operation. The main motivation of this research is to establish suitable model reduction techniques that generate simplified models to capture the essential features of the complex network systems. Two approaches are developed in this thesis to reduce the complexity of a network system with structure preservation. The first one is based on graph clustering, which aims to partition a network into several nonoverlapping clusters and merges all the vertices in each cluster into a single vertex. A reduced-order model is then formulated via the framework of the Petrov-Galerkin projection. This thesis discusses the applications of the clustering-based model reduction methods for second-order networks, controlled power networks, multi-agent systems and directed networks in Part I. The second approach in Part II extends the balanced truncation method for control systems to the simplification of dynamical networks. For networked linear passive systems, the proposed method reduces interconnection structures of a network and the dynamics of each subsystem via a unified framework. Additionally, an approach is developed for the reduction of nonlinear Lur’e networks, showing that the dimension of each nonlinear subsystem can be reduced while preserving the robust synchronization property of the overall network.