Scheduling of Control Nodes for Improved Network Controllability

This paper considers the problem of controlling a linear time-invariant network by means of (possibly) time-varying set of control nodes. As control metric, we adopt the worst-case input energy to drive the network state from the origin to any point on the unit hypersphere in the state space. We provide a geometric interpretation of the controllability Gramian of networks with time-varying input matrices, and establish a connection between the controllability degree of a network and its eigenstructure. Based on the geometric structure of the controllability Gramian, we then propose a scheduling algorithm to select control nodes over time so as to improve the network controllability degree. Finally, we numerically show that, for a class of clustered networks, our algorithm improves upon the performance obtained by a constant set of control nodes, and outperforms an existing heuristic-based on column subset selection.