Robustness of network controllability in cascading failure

It is demonstrated that controlling complex networks in practice needs more inputs than that predicted by the structural controllability framework. Besides, considering the networks usually faces to the external or internal failure, we define parameters to evaluate the control cost and the variation of controllability after cascades, exploring the effect of number of control inputs on the controllability for random networks and scale-free networks in the process of cascading failure. For different topological networks, the results show that the robustness of controllability will be stronger through allocating different control inputs and edge capacity. (C) 2017 Elsevier B.V. All rights reserved.