标题： 块导向多项式系统的精确有限Koopman嵌入 显示英文标题

标题： Exact Finite Koopman Embedding of Block-Oriented Polynomial Systems

摘要： 寻找非线性系统的精确且有限维Koopman嵌入的挑战，已通过采用数据驱动技术来学习不同复杂度的模型（例如，线性、双线性、输入仿射）得到了很大程度的解决。 尽管这些模型可能提供良好的准确性，但选择模型结构和维度仍然是随意的，并且很难量化所引入的误差。 与数据驱动学习的一般趋势相反，本文中，我们开发了一种针对非线性系统的系统性技术，该技术可产生有限维且精确的嵌入。 如果非线性系统被表示为串联和并联的线性和非线性（多项式）模块的网络，可以推导出一个相关的Koopman模型，该模型具有常数状态和输出矩阵，输入影响是多项式的。 此外，如果线性模块没有前馈，Koopman表示将简化为双线性模型。 显示英文摘要

摘要： The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input affine). Although these models may provide good accuracy, selecting the model structure and dimension is still ad-hoc and it is difficult to quantify the error that is introduced. In contrast to the general trend of data-driven learning, in this paper, we develop a systematic technique for nonlinear systems that produces a finite-dimensional and exact embedding. If the nonlinear system is represented as a network of series and parallel linear and nonlinear (polynomial) blocks, one can derive an associated Koopman model that has constant state and output matrices and the input influence is polynomial. Furthermore, if the linear blocks do not have feedthrough, the Koopman representation simplifies to a bilinear model.