The optimal transport paradigm enables data compression in data-driven robust control
This work addresses computational efficiency for uncertain linear time-invariant systems, offering an incremental improvement in data compression for control applications.
The paper tackles the computational burden of data-driven robust control by compressing large datasets into smaller synthetic ones using optimal transport, specifically minimizing Wasserstein distance, and shows that control performance remains comparable with significantly reduced computation.
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.