引用本文:魏纯,徐玲,丁锋.反馈非线性系统随机梯度辨识算法及其收敛性[J].控制理论与应用,2023,40(10):1757~1764.[点击复制]
WEI Chun,XU Ling,DING Feng.Stochastic gradient identification algorithm and its convergence for feedback nonlinear systems[J].Control Theory and Technology,2023,40(10):1757~1764.[点击复制]
反馈非线性系统随机梯度辨识算法及其收敛性
Stochastic gradient identification algorithm and its convergence for feedback nonlinear systems
摘要点击 666  全文点击 229  投稿时间：2021-07-16  修订日期：2023-07-03
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DOI编号  10.7641/CTA.2022.10634
  2023,40(10):1757-1764
中文关键词  反馈非线性系统  双线性参数模型  随机梯度  遗忘因子  收敛性
英文关键词  feedback nonlinear system  bilinear-parameter model  stochastic gradient  forgetting factor  convergence
基金项目  国家自然科学基金项目(62273167)
作者单位E-mail
魏纯 江南大学物联网工程学院 cwei1998@126.com 
徐玲 江南大学物联网工程学院  
丁锋* 江南大学物联网工程学院 fding@jiangnan.edu.cn 
中文摘要
      反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.
英文摘要
      Through the parameterization, we obtain the bilinear-parameter identification model of the feedback nonlinear controlled autoregressive system, which is composed of a controlled autoregressive model in the forward channel and a static nonlinearity in the feedback channel. By decomposing the product term of the bilinear parameters in the identification model, a stochastic gradient identification algorithm is developed to estimate the unknown parameters of the feedback nonlinear system based on the gradient search. In order to improve the convergence rate of the proposed stochastic gradient algorithm, the forgetting factor stochastic gradient algorithm is given by introducing the forgetting factor. Also, this paper establishes the convergence theorem of the parameter estimation and proves the convergence of the proposed stochastic gradient algorithm by means of the stochastic process theory. Finally, the simulation example is carried out to verify the effectiveness of the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance.