  Online feedback optimization is a controller design paradigm for optimizing
the steady-state behavior of a dynamical system. It employs an optimization
algorithm as a dynamic feedback controller and utilizes real-time measurements
to bypass knowing exact plant dynamics and disturbances. Different from
existing centralized settings, we present a fully decentralized feedback
optimization controller for networked systems to lift the communication burden
and improve scalability. We approximate the overall input-output sensitivity
matrix through its diagonal elements, which capture local model information.
For the closed-loop behavior, we characterize the stability and bound the
sub-optimality due to decentralization. We prove that the proposed
decentralized controller yields solutions that correspond to the Nash
equilibria of a non-cooperative game.
