Maximum Correntropy Kalman Filter-Based Robust Model-Free Adaptive Control for MIMO Nonlinear Systems Under Non-Gaussian Noise.

In this article, a robust model-free adaptive control (MFAC) algorithm is proposed based on the maximum correntropy Kalman filter (MCKF) for a class of multiple-input-multiple-output discrete-time nonlinear systems subject to non-Gaussian noise. The proposed algorithm relies solely on input-output data without requiring any model information, effectively suppressing output fluctuations caused by non-Gaussian noise while ensuring satisfactory tracking performance. First, a modified linear data model is constructed using partial-form dynamic linearization (DL). Leveraging this model, a fixed-point iteration-based MCKF is designed to derive posterior output estimates characterized by reduced uncertainty and enhanced smoothness. Subsequently, a cost function involving the posterior tracking error and its difference term is formulated using the posterior output estimates, based on which a robust MFAC algorithm is derived. Furthermore, the mean-square exponential boundedness of the posterior output estimation error and the boundedness of the expectation of the tracking error norm are rigorously established. Finally, the effectiveness and robustness of the proposed algorithm are verified through a numerical simulation and a blast furnace (BF) ironmaking data-based case study.