Sparse allocation of resources in dynamical networks with application to spread control

Sparse resource allocation to shape a network dynamical process is studied. Specifically, we consider allocating limited distributed control resources among a subset of a network´s components, to minimize the dominant eigenvalue of a linear dynamical process associated with the network. Structural characterizations of the closed-loop dynamics at the optimum are obtained. These results are then used to 1) develop constructive algorithms for optimal resource allocation, 2) identify limits on the control performance, and 3) understand the relationship between the network´s graph and the optimal resource profile. This study advances a research thrust on disease spread control in networks, toward the realistic paradigm that control resources can only be allocated at a subset of network locations.