引用本文:萧德云,耿立辉,纪国锋,张益农,农时猛,杨帆,巨辉,刘敏华.基于v-gap达到L2最优的EIV模型频域辨识方法研究[J].控制理论与应用,2025,42(11):2156~2164.[点击复制]
XIAO De-yun,GENG Li-hui,JI Guo-feng,ZHANG Yi-nong,NONG Shi-meng,YANG Fan,JU Hui,LIU Min-hua.Research on frequency-domain identification method of EIV-model based on the v-gap to obtain the L2 optimum[J].Control Theory & Applications,2025,42(11):2156~2164.[点击复制]
基于v-gap达到L2最优的EIV模型频域辨识方法研究
Research on frequency-domain identification method of EIV-model based on the v-gap to obtain the L2 optimum
摘要点击 1649  全文点击 126  投稿时间：2025-02-08  修订日期：2025-10-21
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DOI编号  10.7641/CTA.2025.50049
  2025,42(11):2156-2164
中文关键词  系统辨识  EIV模型  v-gap测度  L2最优准则  频域
英文关键词  system identification  EIV model  v-gap measure  L2 optimum criterion  frequency domain
基金项目  
作者单位E-mail
萧德云 清华大学自动化系 xiaody@tsinghua.edu.cn 
耿立辉 天津职业技术师范大学自动化与电气工程学院  
纪国锋 天津职业技术师范大学自动化与电气工程学院  
张益农 北京联合大学城市轨道交通与物流学院  
农时猛 中国空间技术研究院  
杨帆* 清华大学自动化系 yangfan@tsinghua.edu.cn 
巨辉 成都信息工程大学  
刘敏华 北京市怀柔区委  
中文摘要
      本文论述一类基于v-gap测度、达到实现L2最优的变量带误差(EIV)模型辨识问题,包括单输入单输出系统 的开环与闭环EIV模型辨识和多输入多输出系统的EIV模型辨识.基于v-gap测度就是以扰动模型与逼近模型之间 的距离为优化准则,当满足相应的Nyquist缠绕条件时,获得模型辨识的最优解.达到L2最优是指,在L2空间下对扰 动的输出和输入频域实验数据进行正交分解,使正规右互质因子描述的系统模型的值空间与系统模型补因子描述 的噪声模型的值空间具有正交性,通过优化v-gap测度间接使逼近误差(噪声)达到L2最小.本文所提出的方法 为EIV模型辨识提供了一种新的研究途径,同时适用于闭环系统和多变量系统等多种情况下,不需要对系统输入和 输出有界噪声的特性做任何假设,可以同时估计获得系统模型和相应的噪声模型,在工程上具有广泛的实用性.
英文摘要
      In this paper, a class of errors-in-variables (EIV) model identification problems is discussed based on the v-gap measure to obtain the L2 optimum, and it includes EIV model identification for single input and single output (SISO) open-loop and closed-loop systems as well as multiple input and multiple output (MIMO) systems. Basing the method on the v-gap measure involves considering the distance between the disturbed and approximation models as an optimization criterion and then obtaining the optimal solution to the model identification problem when the corresponding Nyquist winding condition is met. Obtaining the L2 optimum involves performing an orthogonal decomposition in the L2 space of the disturbed output and input frequency-domain experimental data such that the range space of the system model, described by the normalized right coprime factors, is orthogonal to that of the noise model, described by the system model’s complementary factor. The associated approximation error (noise) can then be indirectly minimized in the L2 sense by optimizing the v-gap measure. The proposed method offers a new approach for EIV model identification and is applicable to both closed-loop and multivariable systems. It requires no assumptions about the characteristics of the bounded system input and output noises and can simultaneously estimate the system and associated noise models, making it broadly applicable in engineering practice.