  We consider the controllability of large-scale linear networked dynamical
systems when complete knowledge of network structure is unavailable and
knowledge is limited to coarse summaries. We provide conditions under which
average controllability of the fine-scale system can be well approximated by
average controllability of the (synthesized, reduced-order) coarse-scale
system. To this end, we require knowledge of some inherent parametric structure
of the fine-scale network that makes this type of approximation possible.
Therefore, we assume that the underlying fine-scale network is generated by the
stochastic block model (SBM) -- often studied in community detection. We then
provide an algorithm that directly estimates the average controllability of the
fine-scale system using a coarse summary of SBM. Our analysis indicates the
necessity of underlying structure (e.g., in-built communities) to be able to
quantify accurately the controllability from coarsely characterized networked
dynamics. We also compare our method to that of the reduced-order method and
highlight the regimes where both can outperform each other. Finally, we provide
simulations to confirm our theoretical results for different scalings of
network size and density, and the parameter that captures how much
community-structure is retained in the coarse summary.
