  We study the problem of finite-time constrained optimal control of unknown
stochastic linear time-invariant systems, which is the key ingredient of a
predictive control algorithm -- albeit typically having access to a model. We
propose a novel distributionally robust data-enabled predictive control (DeePC)
algorithm which uses noise-corrupted input/output data to predict future
trajectories and compute optimal control inputs while satisfying output chance
constraints. The algorithm is based on (i) a non-parametric representation of
the subspace spanning the system behaviour, where past trajectories are sorted
in Page or Hankel matrices; and (ii) a distributionally robust optimization
formulation which gives rise to strong probabilistic performance guarantees. We
show that for certain objective functions, DeePC exhibits strong out-of-sample
performance, and at the same time respects constraints with high probability.
The algorithm provides an end-to-end approach to control design for unknown
stochastic linear time-invariant systems. We illustrate the closed-loop
performance of the DeePC in an aerial robotics case study.
