Fixed-time adaptive sliding mode control for nonlinear systems based on rapid Kolmogorov-Arnold network

This paper proposes a fixed-time adaptive sliding mode control method for second-order uncertain nonlinear systems. The proposed controller combines fixed-time nonsingular terminal sliding mode control (FTNSTSMC) with a rapid Kolmogorov-Arnold network (RKAN). Unlike finite-time control, the fixed-time control design provides a settling-time bound that is independent of initial conditions, which makes the convergence process more predictable. A hierarchical nonsingular terminal sliding mode manifold is constructed to improve transient response, avoid singularity, and enhance tracking accuracy. To compensate for unknown nonlinear dynamics, RKAN is introduced as an online approximator. Compared with conventional neural networks, RKAN places learnable activation functions on network edges and uses Gaussian radial basis functions to improve interpretability and computational efficiency. An adaptive robust term is further designed to reduce the influence of approximation errors and external disturbances. The fixed-time stability of the closed-loop system is proved by Lyapunov analysis. Simulations on an inverted pendulum and an active power filter verify the effectiveness of the proposed method. In the active power filter case, the total harmonic distortion is reduced from 33.08% to 0.77%, and the proposed controller achieves an RMSE of 0.8518, an ITAE of 0.0008, and a settling time of 0.0548 s, demonstrating fast convergence, accurate tracking, and strong robustness under disturbances.