  Dynamic mode decomposition (DMD) is a data-driven technique used for
capturing the dynamics of complex systems. DMD has been connected to spectral
analysis of the Koopman operator, and essentially extracts spatial-temporal
modes of the dynamics from an estimate of the Koopman operator obtained from
data. Recent work of Proctor, Brunton, and Kutz has extended DMD and Koopman
theory to accommodate systems with control inputs: dynamic mode decomposition
with control (DMDc) and Koopman with inputs and control (KIC). In this paper,
we introduce a technique, called Network dynamic mode decomposition with
control, or Network DMDc, which extends the DMDc to interconnected, or
networked, control systems. Additionally, we provide an adaptation of Koopman
theory for networks as a context in which to perform this algorithm. The
Network DMDc method carefully analyzes the dynamical relationships only between
components in systems which are connected in the network structure. By focusing
on these direct dynamical connections and cutting out computation for
relationships between unconnected components, this process allows for
improvements in computational intensity and accuracy.
