On controllability of temporal networks

Temporality has been recently identified as a useful feature to exploit when controlling a complex network. Empirical evidence has in fact shown that, with respect to their static counterparts, temporal networks (i) are often endowed with larger reachable sets and (ii) require less control energy when steered towards an arbitrary target state. However, to date, we lack conditions guaranteeing that the dimension of the controllable subspace of a temporal network is larger than that of its static counterpart. In this work, we consider the case in which a static network is input connected but not controllable. We show that when the structure of the graph underlying the temporal network remains the same throughout each temporal snapshot while the (nonvanishing) edge weights vary, then the temporal network will be completely controllable almost always, even when its static counterpart is not. An upper bound on the number of snapshots needed to achieve controllability is also provided.