  Motivated by large-scale but computationally constrained settings, e.g., the
Internet of Things, we present a novel data-driven distributed control
algorithm that is synthesized directly from trajectory data. Our method,
data-driven Distributed and Localized Model Predictive Control (D$^3$LMPC),
builds upon the data-driven System Level Synthesis (SLS) framework, which
allows one to parameterize \emph{closed-loop} system responses directly from
collected open-loop trajectories. The resulting model-predictive controller can
be implemented with distributed computation and only local information sharing.
By imposing locality constraints on the system response, we show that the
amount of data needed for our synthesis problem is independent of the size of
the global system. Moreover, we show that our algorithm enjoys theoretical
guarantees for recursive feasibility and asymptotic stability. Finally, we also
demonstrate the optimality and scalability of our algorithm in a simulation
experiment.
