基于李导数与堆叠回归，从数据中发现非线性系统的反馈线性化模型
Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach
- 用稀疏回归识别系统，再通过李导数构建反馈控制律
- 结合堆叠回归与相对阶条件，实现真实动力学方程的反馈线性化
- 适合做非线性控制建模与数据驱动控制器设计的研究者
发现物理系统的支配方程并设计有效反馈控制器，仍是当前研究中最具挑战性的领域之一。该任务需要深入理解系统行为，包括影响其动态特性的非线性因素。本文提出一种新方法，基于已知先验动态行为识别反馈线性化的物理系统。首先利用稀疏回归算法对系统进行识别，随后通过李导数对输出函数字典应用，推导出一个增强约束，确保不出现内部动态。与以往工作不同，本文创新性地结合了堆叠回归算法与相对阶条件，成功发现并反馈线性化了真实物理模型的支配方程。
原文摘要 · Abstract (English)
Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system behavior, including the nonlinear factors that influence its dynamics. In this article, we propose a novel methodology for identifying a feedback linearized physical system based on known prior dynamic behavior. Initially, the system is identified using a sparse regression algorithm, subsequently a feedback controller is designed for the discovered system by applying Lie derivatives to the dictionary of output functions to derive an augmented constraint which guarantees that no internal dynamics are observed. Unlike the prior related works, the novel aspect of this article combines the approach of stacked regression algorithm and relative degree conditions to discover and feedback linearize the true governing equations of a physical model.
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