引用本文:丁 锋,萧德云,丁 韬.时变系统遗忘因子最小二乘法的有界收敛性（英文）[J].控制理论与应用,2002,19(3):423~427.[点击复制]
DING Feng,XIAO Deyun,DING Tao.Bounded Convergence of Forgetting Factor Least Square Algorithm for Time-Varying Systems[J].Control Theory and Technology,2002,19(3):423~427.[点击复制]
时变系统遗忘因子最小二乘法的有界收敛性（英文）
Bounded Convergence of Forgetting Factor Least Square Algorithm for Time-Varying Systems
摘要点击 1327  全文点击 1199  投稿时间：2000-07-25  修订日期：2001-02-26
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DOI编号  
  2002,19(3):423-427
中文关键词  时变系统  辨识  参数估计  最小二乘  有界收敛性
英文关键词  time-varying system  identification  parameter estimation  least squares  bounded convergence
基金项目  
作者单位E-mail
丁 锋 清华大学 自动化系, 北京 100084 dingf@mail.tsinghua.edu.cn 
萧德云 清华大学 自动化系, 北京 100085 xiaody@mail.tsinghua.edu.cn 
丁 韬 清华大学 自动化系, 北京 100086 dingtao@mails.tsinghua.edu.cn 
中文摘要
      利用随机过程理论研究了遗忘因子最小二乘法 (FFLS)的有界收敛性, 给出了参数估计误差的上界. 分析表明: i)对于时不变确定性系统, FFLS算法产生的参数估计以指数速度收敛于真参数; ii)对于时不变随机系统, FFLS算法给出有界均方估计误差; iii)对于时变随机系统, FFLS算法可以跟踪时变参数, 且跟踪误差有界.
英文摘要
      Based on stochastic process theory, the bounded convergence of forgetting factor least square algorithm (FFLS for short) is studied and the upper bound of the parameter tracking error is given. The analyses indicate that: i) for time-invariant deterministic systems, the estimates given by the FFLS algorithm converge to their true values at exponential rate; ii) for time-invariant stochastic systems, the FFLS algorithm can give a bounded mean square parameter estimation error; iii) for time-varying stochastic systems, the FFLS algorithm may track the time-varying parameters and its parameter tracking error is bounded (that is, the parameter tracking error is small when the parameter change rate is small).