Time-invariant versus time-varying actuator scheduling in complex networks

This paper studies the benefits of time-varying actuator scheduling to the controllability of complex networks. The network dynamics are described by a single-input discrete-time linear system over an undirected graph. Taking the trace of the controllability Gramian as the measure of network controllability, we identify a new notion of nodal communicability and unveil its role in the time-varying actuator scheduling problem. We then proceed to identify conditions on the network structure that determine whether time-varying actuator scheduling is better than time-invariant actuator selection. The main conclusion of our results is that having several and heterogeneous central nodes (versus having a single highly central node) is the common factor in networks where time-varying actuator scheduling is advantageous.