  A new data-enabled control technique for uncertain linear time-invariant
systems, recently conceived by Coulson et\ al., builds upon the direct
optimization of controllers over input/output pairs drawn from a large dataset.
We adopt an optimal transport-based method for compressing such large dataset
to a smaller synthetic dataset of representative behaviours, aiming to
alleviate the computational burden of controllers to be implemented online.
Specifically, the synthetic data are determined by minimizing the Wasserstein
distance between atomic distributions supported on both the original dataset
and the compressed one. We show that a distributionally robust control law
computed using the compressed data enjoys the same type of performance
guarantees as the original dataset, at the price of enlarging the ambiguity set
by an easily computable and well-behaved quantity. Numerical simulations
confirm that the control performance with the synthetic data is comparable to
the one obtained with the original data, but with significantly less
computation required.
