Average Controllability of Cartesian Product Networks

This article explores the average controllability of composite networks generated by factor networks via Cartesian product from energy control perspective, which can be characterized by the controllability Gramian-based metrics. The considered factors are directed weighted networks with diagonalizable / non-diagonalizbable Laplacian dynamics. It is shown that the average controllability of a composite network is determined by the spectral properties of its factors without calculating its own high-dimensional matrix, which reveals how the energy-related controllability of a Cartesian product network (CPN) can be derived from its factors’ features. This will reduce the computational complexity and provide insights to study the energy control of other graph product networks.