Recovering the Controllability of the Temporal Networks

The dynamical interconnected complex systems, whose time scales of dynamics and time scales of the change of the topologies are comparable, are well modeled by the temporal networks. The controllability of the temporal networks are fundamental to the effectiveness and efficiency of their desired functions. For a controllability-damaged temporal network, it is of great significance from the perspective of both theoretic research and industrial engineering to study how to design proper strategies to recover it. In this paper, firstly, the degree of controllability is defined to measure the dimension of the controllable subspace of a temporal network; secondly, two optimal recovering strategies--optimal adding-control-node strategy and optimal adding-temporal-edge strategy--are proposed to recover a controllability-damaged temporal network. Experimental results on various real and model temporal networks show the superiority of these two proposed strategies compared with several other commonly-used recovering strategies.