论文标题

数据驱动控制的行为不确定性量化

Behavioral uncertainty quantification for data-driven control

论文作者

Padoan, Alberto, Coulson, Jeremy, van Waarde, Henk J., Lygeros, John, Dörfler, Florian

论文摘要

本文探讨了数据驱动控制的行为环境中不确定性量化的问题。基于强大控制的经典思想,该问题被认为是选择最适合基于数据的不确定性描述的度量标准的问题。利用Willems的基本引理,有限行为被视为固定维度的子空间,可以用数据矩阵表示。因此,限制行为之间的指标定义为格拉曼尼亚上点之间的距离,即在给定矢量空间中所有相等维的子空间的集合。在限制行为集上定义了一个新的度量标准,是经典差距度量的直接有限时间对应物。表明该度量可以捕获自回旋(AR)类别类别的参数不确定性。数值模拟说明了具有数据驱动模式识别和控制案例研究的新指标的价值。

This paper explores the problem of uncertainty quantification in the behavioral setting for data-driven control. Building on classical ideas from robust control, the problem is regarded as that of selecting a metric which is best suited to a data-based description of uncertainties. Leveraging on Willems' fundamental lemma, restricted behaviors are viewed as subspaces of fixed dimension, which may be represented by data matrices. Consequently, metrics between restricted behaviors are defined as distances between points on the Grassmannian, i.e., the set of all subspaces of equal dimension in a given vector space. A new metric is defined on the set of restricted behaviors as a direct finite-time counterpart of the classical gap metric. The metric is shown to capture parametric uncertainty for the class of autoregressive (AR) models. Numerical simulations illustrate the value of the new metric with a data-driven mode recognition and control case study.

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