Controllability of complex network systems is an active area
of research at the intersection of network science, control theory,
and multi-agent coordination, with multiple applications ranging from
brain dynamics to the smart grid and cyber-physical systems. The basic
question is to understand to what extent the dynamic behavior of the
entire network can be shaped by changing the states of some of its
subsystems, and decipher the role that network structure plays in
achieving this. This talk examines this question in two specific
instances: characterizing network controllability when control nodes
can be scheduled over a time horizon and hierarchical selective
recruitment in brain networks.  Regarding control scheduling, we show
how time-varying control schedules can significantly enhance network
controllability over fixed ones, especially when applied to large
networks.  Through the analysis of a novel scale-dependent notion of
nodal centrality, we show that optimal time-varying scheduling
involves the actuation of the most central nodes at appropriate
spatial scales. Regarding hierarchical selective recruitment, we
examine network mechanisms for selective inhibition and top-down
recruitment of subnetworks under linear-threshold dynamics. Motivated
by the study of goal-driven selective attention in neuroscience, we
build on the characterization of key network dynamical properties to
enable, through either feedforward or feedback control, the targeted
inhibition of task-irrelevant subnetworks and the top-down recruitment
of task-relevant ones.