Error Processing of Sparse Identification of Nonlinear Dynamical Systems via $L_\infty$ Approximation

TL;DR

This paper introduces an $L_ abla$ approximation method for sparse identification of nonlinear dynamical systems, demonstrating improved error handling over traditional $L_2$ approaches through iterative thresholding and experimental validation.

Contribution

It proposes replacing the $L_2$ approximation with $L_ abla$ in SINDy, providing a better description of error phenomena and an effective iterative thresholding algorithm.

Findings

$L_ abla$ approximation outperforms $L_2$ in various error scenarios.

The proposed method effectively handles derivative approximation errors and measurement noise.

Experimental results validate the robustness of $L_ abla$ in SINDy applications.

Abstract

This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the $L_\infty$ approximation could better describe the error phenomenon in the SINDy, which consists of the derivative approximation error and the measurement noise. Then, an iterative thresholding algorithm is proposed to solve the reformulated problem. 3 scenarios of possible errors are considered in the experiment. The results show that the $L_\infty$ approximation performs better or at least equal than the $L_2$ approximation in face of different error cases. Hence, it is reasonable to consider the $L_\infty$ approximation in the applications of the SINDy.