The optimal transport paradigm enables data compression in data-driven robust control

A recently developed robust control technique 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 one 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, albeit enlarging the ambiguity set by an easily computable quantity. Numerical studies 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.