将行为方法拓展到非线性系统建模，实现无需先验识别的直接数据驱动建模。
A Behavioral Framework for Data-Driven Modeling of Nonlinear Systems in Vector-Valued Reproducing Kernel Hilbert Spaces
- 在向量值再生核希尔伯特空间中构建非线性系统的行为框架。
- 结合最小范数插值与子空间辨识，实现直接数据驱动建模。
- 适用于伏尔泰拉系统、哈默斯坦型系统等复杂非线性系统建模。
我们将扬·威廉姆斯的行为方法推广至一类离散时间非线性系统，该类系统定义在向量值再生核希尔伯特空间（RKHS）中。除线性时不变系统外，该类别还涵盖由伏尔泰拉级数及其自回归变体建模的非线性系统，以及具有哈默斯坦型状态空间表示的系统。本文将所提出的框架应用于数据驱动建模问题，即在未知系统上执行仿真或控制任务时，无需显式系统辨识步骤。为此，我们建立了行为方法与两种向量值RKHS中的数据驱动建模方法之间的联系：(1) 最小范数插值，(2) 子空间辨识。
原文摘要 · Abstract (English)
We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled by Volterra series and their autoregressive variants, as well as systems admitting Hammerstein-type state-space realizations. We apply the proposed framework to the problem of data-driven modeling of such systems, i.e., when simulation or control objectives for an unknown system are carried out without an explicit system identification step. To that end, we link the behavioral approach to two data-driven modeling methods in a vector-valued RKHS: (1) minimum-norm interpolation and (2) subspace identification.
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