Strong targeted controllability of dynamical networks

Network controllability is the ability to control the entire network, meaning that we can drive the network from any initial state to any desired final state in finite time by using appropriate inputs which are applied to a subset of nodes of the network. Despite obvious advantages, network controllability is not always feasible as it may ask for a considerable portion of the nodes to be controlled. Moreover, there are cases where controllability of the entire network is not of interest, but rather we are interested in controllability properties of certain parts of the network. This motivates us to investigate the so-called “targeted controllability” of the network, where controllability is only required for a subset of nodes in the network. Noting that targeted controllability can be treated as an output controllability problem, we investigate the (strong) structural output controllability properties of the network from a topological viewpoint. In addition, we examine the structural properties of the reachable subspace of the network. To this end, we use the notion of zero forcing sets, which has been recently exploited in the context of structural controllability.