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

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.