A contraction approach for efficient regulation of networked systems

We present a computationally efficient method for designing regulatory controllers for networked systems using only local information. Using a contraction approach, we derive a connection between a system's intra-dynamics and its neighboring systems. We then show that the design of regulatory controllers is equivalent to a linear feasibility problem on the order of the number of systems. We illustrate our main result using a disturbance mitigation problem, where the goal is to design controllers at a subset of nodes to drive the global nodal values to a particular value in the presence of destabilizing forces. We note that our main result is especially applicable to networks that exhibit interconnection variability and intermittent subsystem faults, like energy grids.