This letter presents a new data-driven controller synthesis based on the Koopman operator and the extended $\mathcal {H}_{2}$ norm characterization of discrete-time linear systems. We model dynamical systems as polytope sets which are derived from multiple data-driven linear models obtained by the finite approximation of the Koopman operator and then used to design robust feedback controllers combined with the $\mathcal {H}_{2}$ norm characterization. The use of the $\mathcal {H}_{2}$ norm characterization is aimed to deal with the model uncertainty that arises due to the nature of the data-driven setting of the problem. The effectiveness of the proposed controller synthesis is investigated through numerical simulations.

中文翻译：

---

基于扩展H2范数表征的数据驱动Koopman控制器综合

这封信提出了一种新的基于Koopman运算符和扩展的数据驱动控制器的综合方法 $ \数学{H} _ {2} $ 离散线性系统的范数刻画。我们将动态系统建模为多面体集，该多面体集是由多个数据驱动的线性模型派生而来的，这些线性模型是通过Koopman算子的有限逼近获得的，然后用于设计与 $ \数学{H} _ {2} $ 规范表征。使用 $ \数学{H} _ {2} $ 规范表征旨在处理由于数据驱动的问题的性质而引起的模型不确定性。通过数值模拟研究了提出的控制器综合的有效性。