数据驱动控制的行为不确定性量化
Behavioral uncertainty quantification for data-driven control
摘要：
本文探讨了数据驱动控制的行为设置中的不确定性量化问题。基于鲁棒控制的经典思想，该问题被认为是选择一个最适合于基于数据的不确定性描述的度量。利用Willems的基本引理，将约束行为看作是固定维数的子空间，可以用数据矩阵表示。因此，受限行为之间的度量被定义为格拉斯曼上的点之间的距离，即，在一个给定的向量空间中所有维数相等的子空间的集合。一个新的度量被定义为一个直接的有限时间对应的经典间隙度量的限制行为的集合。度量捕获参数的不确定性类的自回归（AR）模型。数值模拟与数据驱动的模式识别和控制案例研究说明了新的度量的价值。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
