Adaptive Fractional-Order Sliding-Mode Control with Extended State Observer for Autonomous Underwater Vehicles Under Uncertain Disturbances

In this paper, a composite control framework integrating feedback linearization, an extended state observer, and an adaptive fractional-order sliding-mode controller is presented for autonomous underwater vehicles operating under uncertain hydrodynamics and external disturbances. The proposed algorithm, named adaptive fractional-order sliding-mode control with extended state observer, aims to enhance trajectory-tracking accuracy, disturbance rejection, and robustness against model uncertainties beyond what is offered by conventional active disturbance rejection control and integer-order sliding-mode control. First, a fractional-order sliding surface with an extended state observer is introduced to estimate and compensate lumped disturbances, where the fractional operator provides intrinsic filtering and memory effects to reduce chattering. Second, an adaptive exponential reaching law with smooth switching is formulated to overcome the trade-off between convergence speed and chattering, and a Levant differentiator is employed for sensorless velocity estimation. Finally, the uniform ultimate boundedness of the closed-loop system is proved via Lyapunov stability theory. Comparative simulation studies on step, sinusoidal, and circular trajectories under external disturbances, measurement noise, and 50% parametric uncertainties demonstrate that the proposed controller achieves zero overshoot, suppresses position fluctuations by 97%, and reduces root mean square tracking errors by 38–70% relative to conventional methods, confirming its superior performance.