基于Laguerre滤波器的核范数子空间辨识
Nuclear norm subspace identification based on Laguerre filters
摘要点击 464  全文点击 65  投稿时间:2019-10-11  修订日期:2020-01-14
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DOI编号  10.7641/CTA.2020.90847
  2020,37(12):2663-2670
中文关键词  子空间辨识  Laguerre滤波器  核范数  连续时间随机系统  时不变系统
英文关键词  subspace identification  Laguerre filters  nuclear norm  continuous-time stochastic systems  time-invariant systems
基金项目  国家自然科学基金项目(61773106,61703086,61806079), 流程工业综合自动化国家重点实验室基础科研业务费(2013ZCX02-03)资助
作者单位E-mail
于淼 东北大学秦皇岛分校 yumiao@neuq.edu.cn 
刘建昌 东北大学  
王洪海 东北大学  
张文乐 华东理工大学  
中文摘要
      连续时间随机系统是指各个变量是时间的连续函数并且状态和输出向量受到噪声干扰的动态系统. 由于 生物学、经济学以及物理学等领域都存在连续随机的现象, 连续时间随机系统的辨识受到了各领域专家学者的广 泛关注. 本文针对连续时间随机系统提出一种基于Laguerre滤波器的核范数子空间辨识方法. 首先, 采用Laguerre滤 波器获得系统的输入输出矩阵方程. 然后, 通过核范数最小化方法代替主奇异值的截断获得低秩矩阵逼近, 并利用 交替方向乘子法求解此优化问题. 最后, 采用最小二乘法和残差分析法分别得到模型的系统矩阵和噪声强度. 仿真 结果验证了所提方法的有效性、精确性及比较优势.
英文摘要
      Continuous-time stochastic systems are dynamic systems in which each variable is a continuous function of time and the state and output vectors are disturbed by noise. Due to the existent phenomenon of continuous stochastic in biology, economics and physics, the identification of continuous-time stochastic systems has attracted much attention by experts and scholars in various fields. This paper presents a nuclear norm subspace identification method for continuoustime stochastic systems via Laguerre filters. Firstly, the input-output matrix equation of the systems is deduced by a bank of Laguerre filters. Then, nuclear norm minimization is adopted, instead of the truncation of dominant singular values, to obtain low-rank matrix approximations. Secondly, the optimization problem is solved by the alternating direction method of multipliers. Finally, the system matrices and noise intensity are obtained by the least square method and residual analysis respectively. Simulation results show the efficiency, accuracy and comparative advantage of the proposed method.