一类有色噪声干扰下的随机时变系统学习辨识

Learning identification of a class of stochastic time-varying systems with colored noise

讨论由一类时变ARMAX模型描述的动态系统学习辨识问题,提出用于估计有限区间上重复运行时变系统时变参数的学习算法.文中给出最小二乘学习算法的具体形式及实现步骤,并分析所提出学习算法的收敛性.分析结果表明,当重复持续激励条件成立且满足严格正实条件时,提出的学习算法具有重复一致性,即参数估值完全收敛于真值.文中还将结果推广到一类周期时变系统.通过数值仿真,进一步对所提学习算法的有效性进行了验证.

This paper presents a learning identification method for repetitive systems with time-varying parametric uncertainties.The least squares learning algorithm is derived on the basis of repetitive operations over a pre-specified finite time interval.Sufficient conditions for establishing repetitive consistency of the learning algorithm are given,including the persistent excitation condition and the strictly positive real condition.It is shown that the estimates converge to the time-varying values of the parameters,and the complete estimation can be achieved.The learning identification method is also shown to be applicable to periodically time-varying systems.Numerical simulations are presented to demonstrate the effectiveness of the proposed learning algorithms.