Controllability of multilayer networks

Network controllability recently stimulates researchers' growing interests, and large-scale networked systems in real applications can be well described by multilayer networks. The intrinsic relationship between network controllability and multiple types of connection structures is far from clear and needs further investigations. This paper studies the state controllability of multilayer networks with high-dimensional nodal systems, where the network topology is described by multiple connection structures with different coupling modes. We focus on the impact of multilayer structures, multiple coupling modes, and external control inputs on the controllability of multilayer networked systems, and investigations show that (1) the controllability of multilayer networked system is far more complicated than that of monolayer networked systems and the multilayser topological structures facilitate the controllability; (2) different from that in the monolayer network system, a two-layer network system may be controllable even if both underlying network topologies are uncontrollable. However, under certain conditions, uncontrollable network topologies lead to the two-layer network system being uncontrollable; (3) the mutually complementary coupling modes are beneficial to the controllability of multilayer networks.