论文标题
最小输入设计，用于直接数据驱动的属性识别未知线性系统
Minimum Input Design for Direct Data-driven Property Identification of Unknown Linear Systems
论文作者
论文摘要
在直接数据驱动的方法中，本文研究了{\ em属性识别（ID）}问题，以分析未知的线性系统是否具有感兴趣的属性，例如稳定性和结构属性。与基于模型的分析形成鲜明对比的是，我们通过直接使用未知系统的输入和状态反馈数据进行处理。通过新的输入分段数据丰富的新概念，我们首先建立了最小输入设计的必要条件，以激发属性ID的系统。具体而言，输入截面数据对于属性ID {\ em且仅在}时就足够丰富，它跨越了一个线性子空间，该子空间包含属性依赖性最小线性子空间，其任何基础也可以轻松地用于形成最小激发输入。有趣的是，我们表明可以使用无法识别显式系统模型的最小输入来识别许多结构属性。总体而言，我们的结果严格量化了直接数据驱动分析的优势，而与基于模型的线性系统分析在数据效率方面。
In a direct data-driven approach, this paper studies the {\em property identification(ID)} problem to analyze whether an unknown linear system has a property of interest, e.g., stabilizability and structural properties. In sharp contrast to the model-based analysis, we approach it by directly using the input and state feedback data of the unknown system. Via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum input design to excite the system for property ID. Specifically, the input sectional data is sufficiently rich for property ID {\em if and only if} it spans a linear subspace that contains a property dependent minimum linear subspace, any basis of which can also be easily used to form the minimum excitation input. Interestingly, we show that many structural properties can be identified with the minimum input that is however unable to identify the explicit system model. Overall, our results rigorously quantify the advantages of the direct data-driven analysis over the model-based analysis for linear systems in terms of data efficiency.
