How Training Data Impacts Performance in Learning-Based Control
How Training Data Impacts Performance in Learning-Based Control
复制标题
训练数据如何影响基于学习的控制的性能
作者：
Armin Lederer;A. Capone;Jonas Umlauft;S. Hirche
当由于真实的系统的复杂性而无法导出第一原理模型时，数据驱动的方法允许我们从系统观察中构建模型。由于这些模型被用于基于学习的控制中，数据的质量对所得到的控制律的性能起着至关重要的作用。然而，几乎不存在评估训练数据集的措施，并且数据的空间分布对闭环系统属性的影响在很大程度上是未知的。本文基于高斯过程模型推导出训练数据密度与控制性能之间的解析关系。我们为数据集制定了一个质量度量，我们称之为<inline-formula><tex-math notation="LaTeX">$
h 0 $</tex-math></inline-formula>-gap，并在考虑模型不确定性的情况下，推导出跟踪误差的最终界。我们展示了<inline-formula><tex-math notation="LaTeX">$
HO $</tex-math></inline-formula>-间隙可应用于反馈线性化控制律，并为我们的方法提供了数值例子。
When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data plays a crucial role for the performance of the resulting control law. Nevertheless, there hardly exist measures for assessing training data sets, and the impact of the spatial distribution of the data on the closed-loop system properties is largely unknown. This letter derives — based on Gaussian process models — an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as <inline-formula> <tex-math notation="LaTeX">$
ho $ </tex-math></inline-formula>-gap, and derive the ultimate bound for the tracking error under consideration of the model uncertainty. We show how the <inline-formula> <tex-math notation="LaTeX">$
ho $ </tex-math></inline-formula>-gap can be applied to a feedback linearizing control law and provide numerical illustrations for our approach.