In this paper, we focus on the issue of adaptive fuzzy finite-time tracking control for a class of uncertain fractional-order nonlinear systems with external disturbance. A new finite-time fractional-order command filtered implementation scheme is presented for the adaptive backstepping method. In the command filtered implementation approach, analytical computation of the fractional derivatives of the stabilizing functions is not necessary. Therefore, the controller and adaptive law of the systems are easier to derive and implement. Based on the proposed command filter, adaptive backstepping technique and fractional Lyapunov’s direct method, a novel adaptive fuzzy finite-time controller is designed, which can guarantee that the tracking error converges to a small neighborhood of the origin in finite time, and other signals of the closed-loop systems are semi-global uniform ultimate bounded. In the design process of the controller, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions, and an auxiliary function is adopted to compensate for the unknown external disturbance and approximation errors of FLSs. Finally, a simulation example is given to show the effectiveness and availability of the proposed control strategy.

This paper introduces a novel fixed-time non-singular terminal sliding mode control (NFTTSM) method for addressing the trajectory tracking problem in multi-input multi-output systems subject to uncertainties. First, a fixed-time disturbance observer (FTDO) is designed to compensate for system parameter uncertainties and external disturbances. Subsequently, a variable-gain fixed-time reaching law (VGFTRL), formulated based on a decision function, is proposed to ensure the rapid convergence of the sliding mode variable to the sliding surface, thereby enhancing system robustness. Furthermore, a novel non-singular terminal sliding mode (NNTSM) surface, constructed using the hyperbolic tangent function, is introduced to guarantee that the system state converges to zero within a fixed time along the sliding surface, effectively improving control accuracy while mitigating singularity issues. Building upon FTDO, VGFTRL, and NNTSM, a non-singular fixed-time terminal sliding mode (NFTTSM) controller is developed to ensure that the system state tracks the desired trajectory within a fixed time, with the proposed control scheme ensuring that the tracking time remains independent of initial conditions, thereby offering enhanced control performance. The fixed-time convergence property of the proposed methodology is rigorously established through theoretical analysis. Finally, a manipulator system is applied to validate the feasibility and superiority of the proposed approach, confirming its effectiveness in handling system uncertainties while ensuring precise and robust trajectory tracking.