Networked systems, consisting of distributed nodes that sense their surroundings, exchange information with other nodes, and perform actuation, play an ever-increasing role in applications such as transportation, energy, and health care. In order to provide guarantees on stability and performance, these systems must be controlled via external inputs. An efficient way to do this is by controlling a small subset (leaders) of the network nodes, which then steer the “follower nodes” to the desired state via local interactions. The choice of input nodes will determine critical properties of the system, such as robustness, controllability, and convergence. Selecting a subset of input nodes, however, is inherently a discrete optimization problem, making continuous optimization techniques for control synthesis inapplicable. This talk will describe a submodular optimization framework for selecting the input nodes. Submodularity is a diminishing returns property of discrete functions, analogous to concavity of continuous functions that enables efficient optimization algorithms with provable optimality guarantees.
