Identifiability in the Behavioral Setting
Identifiability in the Behavioral Setting
复制标题
行为环境中的可识别性
DOI：
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复制
发表时间：
2023
影响因子：
6.8
通讯作者：
F. Dörfler
中科院分区：
文献类型：
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作者：
I. Markovsky;F. Dörfler
可识别性，即，识别问题的解的唯一性是系统识别和数据驱动控制中的基本问题。本文给出了确定性线性定常系统可辨识性的充要条件，该系统不需要事先给定变量的输入/输出划分，也不需要真实系统的可控性。可辨识性所需的先验知识是输入的数量、滞后和真实系统的阶数。我们的研究结果是基于修改的概念，一个最强大的不可伪造的有限数据模型和一种新的算法，其计算。我们提供了一个推广的结果，成为众所周知的基本引理和一种新的非参数数据驱动的表示的系统行为的基础上一般的数据矩阵结构。结果假设精确的数据，然而，低秩近似允许他们的应用程序中的噪声数据的情况下。我们比较经验低秩近似的汉克尔，页面，和轨迹矩阵中的误差变量设置。虽然页面和轨迹矩阵是非结构化的，获得的参数估计是不太准确的比从汉克尔矩阵获得的。
Identifiability, i.e., uniqueness of a solution of the identification problem, is a fundamental issue in system identification and data-driven control. Necessary and sufficient identifiability conditions for deterministic linear time-invariant systems that do not require a priori given input/output partitioning of the variables nor controllability of the true system are derived in the article. The prior knowledge needed for identifiability is the number of inputs, lag, and order of the true system. Our results are based on a modification of the notion of a most powerful unfalsified model for finite data and a novel algorithm for its computation. We provide a generalization of a result that became known as the fundamental lemma and a novel nonparametric data-driven representation of the system behavior based on general data matrix structures. The results assume exact data, however, low-rank approximation allows their application in the case of noisy data. We compare empirically low-rank approximation of the Hankel, Page, and trajectory matrices in the errors-in-variables setting. Although the Page and trajectory matrices are unstructured, the parameter estimates obtained are less accurate than the one obtained from the Hankel matrix.
通过矩阵估计进行与模型无关的时间序列分析
DOI：
10.1145/3287319
发表时间：
2018
期刊：
Proceedings of the ACM on Measurement and Analysis of Computing Systems
影响因子：
--
作者：
Agarwal, Anish;Amjad, Muhammad Jehangir;Shah, Devavrat;Shen, Dennis
通讯作者：
Shen, Dennis