Energy-related controllability of corona product networks

Abstract

This article studies the energy-related controllability for a category of ‘large’ composite networks generated by ‘small’ simple factor networks with Laplacian dynamics under a leader-follower framework via corona product. Different from most existing literature on network controllability, this work characterizes the controllability of corona product networks (CPNs) from an energy point of view. This can quantify the difficulty of controlling CPNs based on controllability Gramian measures, involving average controllability and volumetric control energy, etc., where the energy is triggered by the leaders. The energy-related controllability of a CPN can be explored from the eigenvalues and eigenvectors of its factor networks. An algorithm for solving the maximum average controllability is provided, which can help one select the leaders to optimize network control and be applied in practice.