Weighted Learning Identification Method for Hammerstein Nonlinear Time-varying Systems
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摘要: 针对有限区间哈默斯坦(Hammerstein)非线性时变系统，该文提出一种加权迭代学习算法用以估计系统时变参数。首先将Hammerstein系统输入非线性部分进行多项式展开，采用迭代学习最小二乘算法辨识系统的时变参数。为了防止数据饱和，采用带遗忘因子的迭代学习最小二乘算法，进而引入权矩阵，采用加权迭代学习最小二乘算法改进系统跟踪误差，以提高辨识精度。该文分别给出3种算法的推导过程并进行仿真验证。结果表明，与迭代学习最小二乘算法和带遗忘因子迭代学习最小二乘算法相比，加权迭代学习最小二乘算法具有辨识精度高、跟踪误差小以及迭代次数少等优点。Abstract: For Hammerstein nonlinear time-varying systems running repeatedly on finite intervals, a weighted iterative learning algorithm is proposed to estimate the time-varying parameters involved in the system dynamics. The nonlinear input part of the Hammerstein system is tackled based on polynomial expansion, and the iterative learning least square algorithm is given for the time-varying parameter identification. In order to prevent data saturation, an iterative learning least squares algorithm with forgetting factor is proposed for reducing the system tracking error and improving the identification accuracy; A weighted iterative learning least squares algorithm is further presented by introducing the weight matrix. The derivations of the three algorithms are given in detail. The simulation results demonstrate the effectiveness of the proposed learning algorithms, and in comparison with iterative learning least squares algorithm, the modified one sreach high identification accuracy and need fewer iterations.
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表 1 采用加权迭代学习最小二乘算法进行参数估计流程图
输入：重复激励的一组数列 输出：堆积的输出向量${{\boldsymbol{Y}}_k}(t)$ (1) 对于所有的$t = {\text{0,1} },\cdots,N$，给定参数估计的初始值
${\hat \theta _{ - 1}}(t)$=0，迭代所需的${\hat v_k}(t)$,$ {q_1} $及${r_1}$，并置$k = {\text{0}}$;(2) While $k \le {K_{ {\text{max} } } }$(${K_{{\text{max}}}}$为最大迭代次数) (3) for each $t \in [0,N]$ (4) 在第$k$次重复运行时，采集输入数据${u_k}(t)$，计算输出
数据${y_k}(t)$;(5) 计算${{\boldsymbol{Q}}_k}$和${\boldsymbol{\varPhi} } _k^{}(t)[{\hat {\boldsymbol{\phi}} _k}(t)]$; (6) 通过式(46)计算得出${\hat {\boldsymbol{\theta}} _k}(t)$; (7) 利用式(23)更新${\hat v_k}(t)$; (8) End (9) 检验迭代停止条件，满足则停止；否则置$k = k + {\text{1}}$，并回到
第3步；(10) End 
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