For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and the intermediate variable and the states are unmeasurable. To overcome this difficulty, we transform the system from an input nonlinear pseudo-state-space system to an input–output representation and we develop an algorithm based on the Recursive Least Squares, the Levenberg–Marquardt and the Auxiliary Model Principle. The convergence of the identified parameters is studied. The performance of the proposed algorithm are tested by two numerical examples.

中文翻译：

---

分层分数阶 Hammerstein 系统辨识

对于含白噪声的分数阶Hammerstein系统，辨识的难点是线性和非线性块的参数和分数阶未知，中间变量和状态不可测。为了克服这个困难，我们将系统从输入非线性伪状态空间系统转换为输入输出表示，并且我们开发了一种基于递归最小二乘法、Levenberg-Marquardt 和辅助模型原理的算法。研究了识别参数的收敛性。通过两个数值算例对所提算法的性能进行了测试。