标题： 基于核的方法的多步预测器用于通过速度形式的数据驱动非线性系统分析与控制 显示英文标题

标题： Kernel-based multi-step predictors for data-driven analysis and control of nonlinear systems through the velocity form

摘要： 我们提出了基于核的方法来构建非线性（NL）系统的速度形式的单步和多步预测器，该预测器描述了相应非线性系统的时差动力学，并允许高度结构化的表示。 这些预测器反过来可以完全以数据驱动的方式表示速度形式。 我们推导出的基于核的公式，本质上尊重速度形式的结构化准线性和特定的时间相关关系。 这导致了一个高效的速度形式多步预测器，从而也为非线性系统提供了预测器。 此外，通过使用速度形式，我们的方法为具有全局稳定性保证的非线性系统的数据驱动行为分析和控制打开了大门。 显示英文摘要

摘要： We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a highly structured representation. The predictors in turn allow to formulate completely data-driven representations of the velocity form. The kernel-based formulation that we derive, inherently respects the structured quasi-linear and specific time-dependent relationship of the velocity form. This results in an efficient multi-step predictor for the velocity form and hence for nonlinear systems. Moreover, by using the velocity form, our methods open the door for data-driven behavioral analysis and control of nonlinear systems with global stability and performance guarantees.