Time-Varying Actuator Scheduling in Complex Networks

This paper studies the benefit of time-varying actuator scheduling on the controllability of undirected complex networks with linear dynamics. We define a new notion of nodal communicability, termed 2k-communicability, and unveil the role that this centrality measure plays in selecting which nodes to actuate over time to optimize network controllability, as measured by the trace of the controllability Gramian. We identify various conditions on the network structure that determine whether it benefits or not from time-varying actuator scheduling, and quantify the sub-optimality gap of time-invariant policies. Intuitively, our analysis shows that time-varying actuator policies should be used when the network has multiple heterogeneous central nodes, as measured by 2k-communicability. We illustrate our results with examples of deterministic and random networks.