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

TL;DR

This paper introduces an optimal transport-based data compression method for data-driven robust control of uncertain linear systems, reducing computational load while maintaining performance guarantees.

Contribution

It develops a novel optimal transport approach to compress large datasets into synthetic ones, enabling efficient control without sacrificing robustness.

Findings

Synthetic data achieves comparable control performance to original data.

Computational complexity is significantly reduced with the compressed dataset.

Performance guarantees are preserved despite data compression.

Abstract

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.