引用本文:丁 锋，杨家本.关于鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析[J].控制理论与应用,1999,16(4):569~572.[点击复制]
Ding Feng and Yang Jiaben.Remarks on Martingale Hyperconvergence Theorem and the Convergence Analysis of the Forgetting Factor Least Squares Algorithms[J].Control Theory and Technology,1999,16(4):569~572.[点击复制]
关于鞅超收敛定理与遗忘因子最小二乘算法的收敛性分析
Remarks on Martingale Hyperconvergence Theorem and the Convergence Analysis of the Forgetting Factor Least Squares Algorithms
摘要点击 1540  全文点击 401  投稿时间：1997-02-28  修订日期：1998-07-07
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DOI编号  
  1999,16(4):569-572
中文关键词  时变系统  鞅收敛定理  反馈线性化  参数估计  最小二乘算法
英文关键词  time-varying system  martingale convergence theorem  martingale hyperconvergence theorem  parameter estimation  least squares algorithm
基金项目  
作者单位
丁 锋，杨家本  
中文摘要
      鞅超收敛定理是研究随机时变系统辨识算法有界收敛性的一个有效数学工具，它是鞅收敛定理在随机时变系统中推广.文[1]用它证明了遗忘因子最小二乘算法参数估计误差的有界收敛性.但是文[1]假设系统的输入输出信号是各态遍历的，且协方差阵是用它的数字期望数值代替的，所感应电机得到的结果是近似值.而本文精确地给出了协方差阵的上下界，改进了文[1]的结果.
英文摘要
      The martingale hyperconvergence theorem(MHCT) is an mathematical tool of analyzing the bounded convergence of identification algorithms and the extension of the martingale convergence theorem in stochastic time-varying systems.The upper boundedness of the parameter estimation error of forgetting factor least squares algorithms was given by using (MHCT) in Ref.[1],but the upper boundedness of the covariance matrix was replacecd with its expectation approximately. In this paper the upper and lower boundedness of the covariance matrix is given and the results of Ref.[1] are improved.