  A data-driven MPC scheme is proposed to safely control constrained stochastic
linear systems using distributionally robust optimization. Distributionally
robust constraints based on the Wasserstein metric are imposed to bound the
state constraint violations in the presence of process disturbance. A feedback
control law is solved to guarantee that the predicted states comply with
constraints. The stochastic constraints are satisfied with regard to the
worst-case distribution within the Wasserstein ball centered at their discrete
empirical probability distribution. The resulting distributionally robust MPC
framework is computationally tractable and efficient, as well as recursively
feasible. The innovation of this approach is that all the information about the
uncertainty can be determined empirically from the data. The effectiveness of
the proposed scheme is demonstrated through numerical case studies.
