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.

中文翻译：

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最佳传输范式可在数据驱动的稳健控制中实现数据压缩

最近由 Coulson 等人构想的一种用于不确定线性时不变系统的新的数据启用控制技术建立在控制器对从大型数据集提取的输入/输出对上的直接优化的基础上。我们采用基于最佳传输的方法将如此大的数据集压缩为具有代表性行为的较小合成数据集，旨在减轻要在线实现的控制器的计算负担。具体来说，合成数据是通过最小化原始数据集和压缩数据集支持的原子分布之间的 Wasserstein 距离来确定的。我们表明，使用压缩数据计算的分布鲁棒控制律享有与原始数据集相同类型的性能保证，以扩大由易于计算且表现良好的数量设置的模糊性为代价。数值模拟证实，合成数据的控制性能与原始数据获得的控制性能相当，但所需的计算量明显减少。