Controllability of Deep-Coupling Dynamical Networks

This paper explores the state controllability of deep-coupling networks with inter-layer couplings, where the nodes of each layer are higher-dimensional linear time-invariant dynamical systems. The collective effects on the network controllability from intra-layer network topologies, node dynamics, external control inputs and inner interactions are extensively explored under two representative inter-layer coupling modes, where the integrated network can be controllable even if the intra-layer network topology is uncontrollable by external inputs. Some necessary and/or sufficient conditions for the network controllability are obtained for the representative two-layer intra-layer couplings of interdependent and drive-response modes. Simulated examples reveal the important role of inter-layer couplings of a controllable deep-coupling dynamical network assembled from uncontrollable intra-layer networks.