  We present a robust Distributed and Localized Model Predictive Control
(rDLMPC) framework for large-scale structured linear systems. The proposed
algorithm uses the System Level Synthesis to provide a distributed closed-loop
model predictive control scheme that is robust to exogenous disturbances. The
resulting controllers require only local information exchange for both
synthesis and implementation. We exploit the fact that for polytopic
disturbance constraints, SLS- based distributed control problems have been
shown to have structure amenable for distributed optimization techniques. We
show that similar to the disturbance-free DLMPC algorithm, the computational
complexity of rDLMPC is independent of the size of the global system. To the
best of our knowledge, robust DLMPC is the first MPC algorithm that allows for
the scalable distributed computation of distributed closed-loop control
policies in the presence of additive disturbances.
