Fixed‐time convergence non‐singular disturbance rejection control for high‐order uncertain nonlinear systems

Traditional control methods for high‐order nonlinear systems often exhibit slow convergence and poor robustness. To address these challenges, this paper proposes a fixed‐time convergence non‐singular disturbance rejection control strategy tailored for high‐order nonlinear systems. First, by integrating power functions and exponential functions, a novel fixed‐time fast‐convergence Lyapunov function is constructed based on finite‐time control theory. This function guarantees a fixed upper bound for the system's convergence time, independent of the system's initial states. Compared to conventional finite‐time Lyapunov functions, the proposed approach achieves significantly faster convergence rates. Subsequently, this function is combined with a backstepping control strategy, and a nonlinear disturbance observer is employed to accurately estimate the combined effects of unknown disturbances and modeling errors. This method enhances the controller's response speed, improves disturbance rejection capabilities, and reduces steady‐state errors. Finally, the proposed control strategy is applied to an inverted pendulum system and a hydraulic servo system. Experimental results demonstrate that the proposed strategy offers significant performance advantages.