Hammerstein-Wiener时变系统的带遗忘因子学习辨识算法

Iterative learning algorithm with forgetting factor for Hammerstein-Wiener time-varying systems

针对一类有限区间上重复运行的Hammerstein-Wiener非线性时变系统,将Hammerstein-Wiener系统输出非线性部分进行多项式展开以构造回归模型,采用带遗忘因子迭代学习梯度算法和带遗忘因子迭代学习最小二乘算法,估计系统的时变参数。当系统参数沿时间轴快变、沿迭代轴缓变时,修正遗忘因子提高算法的辨识精度。文中分别给出了2种算法的推导过程并进行仿真对比验证,结果表明,带遗忘因子迭代学习最小二乘算法收敛速度更快、精度更高,达到相同性能指标时所需迭代次数更少,验证了所提学习算法的有效性。

For Hammerstein-Wiener nonlinear time-varying systems running repeatedly on a finite interval,the nonlinear output part of Hammerstein-Wiener system is tackled based on polynomial expansion to construct the regression model.The time-varying parameters of the system are estimated by the iterative learning gradient algorithm with forgetting factor and the iterative learning least square algorithm with forgetting factor.When the system parameters change rapidly along the time axis and slowly along the iteration axis,the forgetting factor is modified to improve the identification accuracy.The derivation processes of the two algorithms are given and verified by numeral simulations.The simulation results show that the iterative learning least squares algorithm with forgetting factor can perform high identification accuracy,fast convergence speed and few iterations when reaching the same performance index,which verifies the effectiveness of the proposed learning algorithm.