在Loewner框架中识别低订单系统
Arya Honarpisheh1, Rajiv Singh2, Jared Miller3
1ECE Dept., Northeastern University, Boston, MA 02115 USA.
IFAC-PapersOnLine
|August 20, 2025
概括
这项研究引入了一种从实验数据中识别低级系统模型的新方法. 基于Loewner的方法提供更快的单值衰减,与传统的汉克尔矩阵方法相比,产生更高效的模型.
科学领域:
- 系统工程
- 控制理论
- 数字分析
背景情况:
- 准确的系统识别对于控制和分析至关重要.
- 传统的方法,如基于汉克尔矩阵的识别,可以计算密集,并产生高阶模型.
- 根据时间域数据进行非参数识别具有独特的挑战.
研究的目的:
- 开发一种新的非参数方法,从时间域数据中识别低级系统模型.
- 为了比较基于Loewner的插入和减少的效率与传统的汉克尔矩阵方法.
- 通过数值示例来证明拟议方法的有效性.
主要方法:
- 使用基于卡拉西奥多里·费杰和洛恩的插值来实现系统.
- 应用Loewner矩阵平衡减少 (LBR) 步骤进行模型订单减少.
- 使用Zolotarev数来分析单数值衰减率.
主要成果:
- 罗纳矩阵作为一个有效的系统的痕迹规范估计器.
- 洛纳矩阵中的奇点值比汉克尔矩阵中的显著更快的衰变率.
- 基于Loewner的方法可以实现具有可比错误极限的低级系统模型.
结论:
- 提出的基于Loewner的方法为非参数系统的识别提供了更有效的方法.
- 这种技术可以提高精度和计算效率.
- 这些发现为各种工程应用中的系统识别提供了有价值的替代方案.
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