论文标题
线性系统的精密数据启用Koopman型逆运算符
Precision Data-enabled Koopman-type Inverse Operators for Linear Systems
论文作者
论文摘要
轻松访问大量数据的出现引发了人们对直接发展动态系统输入与输出之间关系的兴趣。一个挑战是，除了应用输入和测量的输出外，动力学还可以取决于未直接测量的隐藏状态。这项工作的主要贡献是确定所需的信息（尤其是输出的过去历史），以删除koopman型逆运算符中的隐藏状态依赖性。此外，可以证明，应使用输出的瞬时时间导数来增加输出的时间历史，以实现逆运算符的精确度。用示例系统说明了对删除隐藏状态依赖并提高启用数据启用逆运算符精度的所需输出（历史和瞬时导数）信息的洞察力。
The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the dynamics can also depend on hidden states that are not directly measured. The main contribution of this work is to identify the information needed (in particular, the past history of the output) to remove the hidden state dependence in Koopman-type inverse operators for linear systems. Additionally, it is shown that the time history of the output should be augmented with the instantaneous time derivatives of the output to achieve precision of the inverse operator. This insight into the required output (history and instantaneous derivative) information, to remove the hidden-state dependence and improve the precision of data-enabled inverse operators, is illustrated with an example system.
