A Robust Kernel‐Based Global Identification Method for Hammerstein Parameters Varying System With Non‐Gaussian Output Noises

ABSTRACT The Hammerstein parameters varying system (HPVS) with output noises is studied for dynamic processes in the paper. It has a cascaded structure of Hammerstein models, and its parameters are dependent on a time‐varying variable known as the scheduling variable, while also considering non‐Gaussian output noises. We present a robust kernel‐based global identification method (RKGIM) by using kernel methods and expectation maximization variational inference (EMVI) algorithm. Firstly, a Gaussian process (GP) with a radial basis kernel is considered to model the dependence of HPVS's parameters on scheduling variables, and a noise‐like term is introduced for numerical reasons. Their union designs a prior distribution for the system's noise‐free output, providing a possible description of the HPVS's output on scheduling variables. Then, to ensure the robustness of the identification, the measurement noise is described as a parametric Student's t distribution rather than the traditional Gaussian distribution. Furthermore, in the EMVI framework, the E‐step estimates the posterior estimations of the noise parameters and noise‐free output by using VI, while the M‐step estimates the hyperparameters that determine the aforementioned kernel by maximizing the likelihood. Finally, the effectiveness of the proposed method is demonstrated by simulation experiments.