基于滤波的分段线性Hammerstein系统的递推辨识方法

Filtering-based recursive identification methods for piecewise-linear Hammerstein systems

Hammerstein模型具有结构简单、能很好地反映典型非线性特性等优点,一直是控制领域的重要研究内容之一.本文主要研究输出误差自回归Hammerstein系统的辨识问题,系统的输入非线性部分采用分段线性函数拟合,并引入切换函数和位置函数将其表示为线性参数表达式.为克服有色噪声的干扰,本文通过关键项分离和数据滤波技术,建立系统的滤波辨识模型.在此基础上,文中提出了基于滤波的遗忘梯度算法,基于滤波的递推广义最小二乘算法和基于滤波的多新息遗忘梯度算法估计未知参数.本文通过仿真实例验证了所提算法的有效性,证明了多新息理论的应用可以有效地提高递推算法的辨识性能.

Hammerstein models have always been the research focus on control field for their advantages of simple structures and can reflect typical nonlinear characteristics.This paper mainly studies the identification problems of the Hammerstein output-error autoregressive systems.The input nonlinear part of the system is described by piecewise-linear functions and expressed as a parametric linear expression by introducing a switching function and position functions.For overcoming the interference of colored noise,we derive the filtering identification model of the system through the key item separation and the data filtering technique.On the basis of this model,the filtering-based forgetting gradient algorithm,the filtering-based recursive generalized least-squares algorithm and the filtering-based multi-innovation forgetting gradient algorithm are presented for estimating the unknown parameters.A simulation example is given to test the effectiveness of the proposed algorithms and demonstrates that the identification performance of the recursive identification algorithms can be improved effectively through the application of the multi-innovation identification theory.