Model Reduction of Networks Preserving the Network First and Second Order Structure

Abstract

Network systems have received a lot of attention in the past decade. They are used to analyze and design communication network, smart grid technology, social media, social dynamics, formation and consensus problems, etc. Several analysis and control methods have been developed for network systems. However, often, their large scale nature makes it difficult to analyze and to design a controller. We develop methods to reduce the order of the network while preserving the network structure, as well as some structure of the (linear) node dynamics. In particular, second order network dynamics structure is preserved. We use node clustering methods, as well as a state space singular value decomposition based method. For the first we provide error bounds. We illustrate the results with help of some relevant high order examples.