  In this paper, we study a data-enabled predictive control (DeePC) algorithm
applied to unknown stochastic linear time-invariant systems. The algorithm uses
noise-corrupted input/output data to predict future trajectories and compute
optimal control policies. To robustify against uncertainties in the
input/output data, the control policies are computed to minimize a worst-case
expectation of a given objective function. Using techniques from
distributionally robust stochastic optimization, we prove that for certain
objective functions, the worst-case optimization problem coincides with a
regularized version of the DeePC algorithm. These results support the
previously observed advantages of the regularized algorithm and provide
probabilistic guarantees for its performance. We illustrate the robustness of
the regularized algorithm through a numerical case study.
