论文标题
线性系统结构特性的嘈杂数据的信息
Informativity of noisy data for structural properties of linear systems
论文作者
论文摘要
本文介绍了开发用于检查未知系统是否具有某些结构属性的测试。我们所针对的测试是根据从未知系统获得的嘈杂输入状态输出数据来看的。由于总体而言，数据并不能独特地确定未知系统，因此许多系统与相同的数据集兼容。因此，我们无法应用系统标识并应用现有的基于模型的测试。取而代之的是，我们将使用信息性概念，并为给定的嘈杂数据建立测试。我们将对一系列系统属性进行此操作，其中包括强可观察性，可检测性以及强大的可控性和稳定性。这些信息性测试将根据可以从嘈杂数据构建的多项式矩阵的等级测试。我们还将建立一个用于信息分析的几何框架。在该框架内，我们将提供几何测试，以提供强大可观察性，可观察性和左右插头的信息。
This paper deals with developing tests for checking whether an unknown system has certain structural properties. The tests that we are aiming at are in terms of noisy input-state-output data obtained from the unknown system. Since, in general, the data do not determine the unknown system uniquely, many systems are compatible with the same set of data. Therefore we can not apply system identification and apply existing, model based, tests. Instead, we will use the concept of informativity, and establish tests for informativity of the given noisy data. We will do this for a range of system properties, among which strong observability and detectability and strong controllability and stabilizability. These informativity tests will be in terms of rank tests on polynomial matrices that can be constructed from the noisy data. We will also set up a geometric framework for informativity analysis. Within that framework we will give geometric tests for informativity for strong observability, observability, and left-invertibilty.
