Fixed-Point Kernel Adaptive Filtering for Fractional-Order Nonlinear Dynamical Systems With Applications to Chaotic Circuits

Existing adaptive filtering methods encounter significant challenges in simultaneously ensuring accurate prediction and robust stability when applied to real-time dynamic modeling of fractional-order nonlinear systems. To address these limitations, this paper proposes the fixed-point kernel least mean squares (FPKLMS) algorithm, which extends classical kernel adaptive filtering by introducing a novel fixed-point iteration strategy. Specifically, the proposed algorithm reformulates the weight update mechanism as a fixed-point problem in the reproducing kernel Hilbert space (RKHS), while accommodating structural variations in the weight updating operator. Through rigorous theoretical analysis, we establish the global convergence of the FPKLMS algorithm and derive explicit convergence rate bounds under mild assumptions. Experiments on fractional-order Chua’s and Lorenz circuits demonstrate that the FPKLMS algorithm achieves superior robustness, stability, and real-time prediction performance over existing methods. This approach provides an efficient and reliable framework for real-time modeling of fractional-order nonlinear dynamic systems, effectively addressing the dual requirements of accurate prediction and robust stability.