  Control of large-scale networked systems often necessitates the availability
of complex models for the interactions amongst the agents. However in many
applications, building accurate models of agents or interactions amongst them
might be infeasible or computationally prohibitive due to the curse of
dimensionality or the complexity of these interactions. In the meantime,
data-guided control methods can circumvent model complexity by directly
synthesizing the controller from the observed data. In this paper, we propose a
distributed Q-learning algorithm to design a feedback mechanism based on a
given underlying graph structure parameterizing the agents' interaction
network. We assume that the distributed nature of the system arises from the
cost function of the corresponding control problem and show that for the
specific case of identical dynamically decoupled systems, the learned
controller converges to the optimal Linear Quadratic Regulator (LQR) controller
for each subsystem. We provide a convergence analysis and verify the result
with an example.
