论文标题
在连续时间版本的Willems的引理
On a Continuous-Time Version of Willems' Lemma
论文作者
论文摘要
在本文中，提出了一种表示连续时间线性系统的每个输入输出轨迹的方法。这对应于著名的Willems的引理的连续时间版本。结果是通过定期抽样连续信号并构建非常类似于离散时间对应物的汉克尔样结构来获得的。然后，它显示了如何使用测量的持续激发数据来设计参数的时变向量，从而允许生成任意分段可区分的轨迹。还提供了满足持续激发条件的一类输入信号。
In this paper, a method to represent every input-output trajectory of a continuous-time linear system in terms of previously collected data is presented. This corresponds to a continuous-time version of the well-known Willems' lemma. The result is obtained by sampling the continuous signals at regular intervals, and constructing Hankel-like structures that closely resemble their discrete-time counterparts. Then, it is shown how to use measured persistently excited data to design a time-varying vector of parameters that allows the generation of arbitrary piecewise differentiable trajectories. A class of input signals that satisfies the conditions for persistence of excitation is also provided.
