  Feedback optimization is an increasingly popular control paradigm to optimize
dynamical systems, accounting for control objectives that concern the system's
operation at steady-state. Existing feedback optimization techniques heavily
rely on centralized system and controller architectures, and thus suffer from
scalability and privacy issues when systems become large-scale. In this paper,
we propose and study a distributed architecture for feedback optimization, in
which each agent updates its local control state by combining the average of
its neighbors with a local negative-gradient step. Under convexity and
smoothness assumptions, we establish convergence of the control method to a
fixed point. By reinforcing the assumptions to restricted strong convexity of
the cost, we show that our algorithm converges linearly to a neighborhood of
the optimal point, where the size of the neighborhood depends on the choice of
the stepsize. Simulations corroborate the theoretical results.
