  The System Level Synthesis (SLS) approach facilitates distributed control of
large cyberphysical networks in an easy-to-understand, computationally scalable
way. We present an overview of the SLS approach and its associated extensions
in nonlinear control, MPC, adaptive control, and learning for control. To
illustrate the effectiveness of SLS-based methods, we present a case study
motivated by the power grid, with communication constraints, actuator
saturation, disturbances, and changing setpoints. This simple but challenging
case study necessitates the use of model predictive control (MPC); however,
standard MPC techniques often scales poorly to large systems and incurs heavy
computational burden. To address this challenge, we combine two SLS-based
controllers to form a layered MPC-like controller. Our controller has constant
computational complexity with respect to the system size, gives a 20-fold
reduction in online computation requirements, and still achieves performance
that is within 3% of the centralized MPC controller.
