Data-driven modeling and parameter estimation of Nonlinear systems

TL;DR

This paper presents a new data-driven method using trust region optimization for accurately modeling and estimating parameters of nonlinear systems, demonstrated on systems like Van der Pol, Damped oscillator, and Lorenz system.

Contribution

It introduces a novel approach for nonlinear system parameter estimation that improves accuracy and robustness over existing methods.

Findings

Effective parameter identification for nonlinear systems

Successful application to chaotic Lorenz system

Potential for real-world nonlinear system modeling

Abstract

Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel data-driven approach for accurately modeling and estimating parameters of nonlinear systems utilizing trust region optimization. The proposed method is applied to three well-known systems: the Van der Pol oscillator, the Damped oscillator, and the Lorenz system, which find broad applications in engineering, physics, and biology. The results demonstrate the efficacy of the approach in accurately identifying the parameters of these nonlinear systems, enabling a reliable characterization of their behavior. Particularly in chaotic systems like the Lorenz system, capturing the dynamics on the attractor proves to be crucial. Overall, this article presents a robust data-driven approach for parameter estimation in nonlinear dynamical systems, holding promising potential for real-world applications.