Control-capacity analysis and optimized construction for controlled interdependent networks

In order to obtain interdependent networks with stronger control-capacity, in this paper, based on Kalman’s rank theory, a widely used and improved index of control-capacity for controlled interdependent networks is firstly analyzed and proposed theoretically, and two examples are employed to show the feasibility and effectiveness of this presented index. Secondly, with this index, the influence of the intra-couplings, network scale, inter-coupling strength, inter-couplings, and controllers on the control-capacity of sixteen controlled interdependent networks with two subnets, which are any combination of BA scale-free network, WS small-world network, NW small-world network and ER random network, are analyzed and discussed, as well as their optimal structures and various parameters for best control-capacity. Finally, with this index proposed, a novel algorithm is put forward to build up interdependencies or inter-couplings to enhance the control-capacity of controlled interdependent networks. The simulations show that the algorithm designed in this paper is feasible and effective, and can achieve interdependent networks with stronger control-capacity. •A modified index is presented to measure the control-capacity of controlled interdependent networks.•The control-capacity of sixteen controlled networks is analyzed and discussed.•Several factors related to the networks are investigated, as well as their optimized parameters.•An algorithm for establishing optimized inter-couplings is proposed.•Newly constructed interdependent networks perform better with optimized control-capacity.