Integral Formulation of QENDy for Robust Nonlinear System Identification

2026-06-09

AI Summary

This work addresses the poor robustness of traditional QENDy methods in noisy environments, which stems from their reliance on time derivatives and leads to inaccurate identification of nonlinear system dynamics. To overcome this limitation, the paper proposes a novel integral-form QENDy approach that, for the first time, incorporates an integral operator into the quadratic embedding framework. By eliminating the explicit computation of time derivatives and relying solely on raw trajectory data, the method achieves system identification with high accuracy while significantly enhancing robustness against measurement noise. This advancement offers a more reliable pathway for modeling nonlinear systems in practical engineering applications where data are often corrupted by noise.

Abstract

This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory data points along with their time derivatives are used. Methods for calculating time derivatives make the algorithm sensitive to noise. Our integral formulation does not use the time derivatives. This results in a more robust method to learn the dynamics.

Problem

• nonlinear system identification
• QENDy
• time derivatives
• noise sensitivity
• robustness

Innovation

• integral formulation
• QENDy
• nonlinear system identification
• noise robustness
• quadratic embedding