Extended H _∞ Filtering in RKHS for Nonlinear Systems With Uncertainty

Uncertainties in nonlinear systems can significantly hinder the effectiveness of traditional filtering methods, leading to suboptimal state estimation and compromising overall performance and robustness. Therefore, an extended H<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\infty }$ </tex-math></inline-formula> filtering based on reproducing kernel Hilbert space (RKHS) is proposed for addressing the state estimation issue existing in the nonlinear system with uncertainty in this brief. In particular, this extended H<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\infty }$ </tex-math></inline-formula> filtering is derived in RKHS by using conditional embedding operator and a robust optimization framework. In addition, it employs an adaptive kernel size method to enhance the model’s generalization capability. Moreover, an online sampling method based on Nyström approach is utilized to reduce computational complexity. Simulation results in chaotic time series prediction and SOC estimation demonstrate that the proposed algorithm outperforms the other competitive algorithms.