论文标题
最佳传输范式可以在数据驱动的鲁棒控制中启用数据压缩
The optimal transport paradigm enables data compression in data-driven robust control
论文作者
论文摘要
Coulson et \ al。最近构想的一种不确定线性时间不变的系统的新的启用数据的控制技术建立在从大型数据集中绘制的输入/输出对的直接优化控制器的基础上。我们采用一种最佳的基于运输的方法将如此大的数据集压缩到代表性行为的较小合成数据集中，旨在减轻要在线实施的控制器的计算负担。具体而言，通过最小化原始数据集和压缩的原子分布之间的Wasserstein距离来确定合成数据。我们表明，使用压缩数据计算出的分配强大的控制法律享有与原始数据集相同类型的性能保证，价格为扩大易于计算且易于计算的数量设置的歧义。数值模拟证实，具有合成数据的控制性能与原始数据获得的控制性能相当，但需要较少的计算。
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.
