Title: Data-driven modeling and parameter estimation of Nonlinear systems Show Chinese title

Title: 数据驱动的非线性系统建模与参数估计

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. Show Chinese abstract

Abstract: 非线性系统在众多科学和工程学科中扮演着重要角色，理解其行为对于制定有效的控制和预测策略至关重要。 本文介绍了一种基于信任域优化的新颖数据驱动方法，用于准确建模和估计非线性系统的参数。 该方法应用于三个著名的系统：Van der Pol 振荡器、阻尼振荡器以及洛伦兹系统，这些系统在工程学、物理学和生物学中有着广泛的应用。 结果表明，该方法能够准确识别这些非线性系统的参数，从而可靠地表征它们的行为。 特别是在像洛伦兹系统这样的混沌系统中，捕获吸引子上的动力学显得尤为关键。 总体而言，本文提出了一种针对非线性动态系统参数估计的强大数据驱动方法，在现实世界应用中具有广阔的潜力。