This article focuses on the parameter estimation problem of the input nonlinear system where an input variable‐gain nonlinear block is followed by a linear controlled autoregressive subsystem. The variable‐gain nonlinearity is described analytical by using an appropriate switching function. According to the gradient search technique and the auxiliary model identification idea, an auxiliary model‐based stochastic gradient algorithm with a forgetting factor is presented. For the sake of improving the parameter estimation accuracy, an auxiliary model gradient‐based iterative algorithm is proposed by utilizing the iterative identification theory. To further optimize the performance of the algorithm, we decompose the identification model of the system into two submodels and derive a two‐stage auxiliary model gradient‐based iterative (2S‐AM‐GI) algorithm by using the hierarchical identification principle. The simulation results confirm the effectiveness of the proposed algorithms and show that the 2S‐AM‐GI algorithm has higher identification efficiency compared with the other two algorithms.

中文翻译：

---

输入非线性控制的具有可变增益非线性的自回归系统的两阶段基于辅助模型梯度的迭代算法

本文重点介绍输入非线性系统的参数估计问题，其中输入变量增益非线性块后面是线性控制的自回归子系统。通过使用适当的开关函数来分析变增益非线性。根据梯度搜索技术和辅助模型识别思想，提出了一种具有遗忘因子的基于辅助模型的随机梯度算法。为了提高参数估计精度，利用迭代识别理论，提出了一种基于辅助模型梯度的迭代算法。为了进一步优化算法的性能，我们将系统的识别模型分解为两个子模型，并使用分层识别原理导出基于梯度的两阶段辅助模型迭代（2S-AM-GI）算法。仿真结果证实了所提算法的有效性，表明2S‐AM‐GI算法与其他两种算法相比具有更高的识别效率。