  Networked systems are systems of interconnected components, in which the
dynamics of each component are influenced by the behavior of neighboring
components. Examples of networked systems include biological networks, critical
infrastructures such as power grids, transportation systems, and the Internet,
and social networks. The growing importance of such systems has led to an
interest in control of networks to ensure performance, stability, robustness,
and resilience. A widely-studied method for controlling networked systems is to
directly control a subset of input nodes, which then steer the remaining nodes
to their desired states. This article presents submodular optimization
approaches for input node selection in networked systems. Submodularity is a
property of set functions that enables the development of computationally
tractable algorithms with provable optimality bounds. For a variety of
physically relevant systems, the physical dynamics have submodular structures
that can be exploited to develop efficient input selection algorithms. This
article will describe these structures and the resulting algorithms, as well as
discuss open problems.
