This study focuses on addressing the the coupling problem of the vertical and horizontal plane of an autonomous underwater vehicle (AUV) with an X-rudder. To guarantee the steering performance of the AUV, a depth and course control algorithm based on an $L_1$ adaptive control algorithm (L1AC) is proposed. Firstly, the linear quadratic regulator (LQR) is designed on the basis of an AUV vertical and horizontal linear model, and the system has optimal control quality for both of the nominal vertical and horizontal models. Secondly, the nonlinear state predictor, disturbance estimator, and adaptive controller are designed separately, which is used for the compensation of the uncertainty and disturbance of the AUV dynamic. Finally, the rudder angle allocation algorithm is designed to realize the rudder angle command of the cross rudder to the X-rudder. The simulation and experiment results show that the adaptive control algorithm proposed in this paper can effectively control AUV to complete high-performance course and depth control. Based on the experiments, the prospects and shortcomings of the L1AC, LQR and MRAC algorithm in AUV control are compared and analyzed.

Aiming at the control challenges faced by unmanned surface vessels (USVs) in complex environments, such as nonlinearities, parameter uncertainties, and environmental perturbations, we propose a non-singular terminal integral sliding mode control strategy based on an extended state observer (ESO). The strategy first employs a third-order linear extended state observer to estimate the total disturbances of the USV system, encompassing both external disturbances and internal nonlinearities. Subsequently, a backstepping sliding mode controller based on the Lyapunov theory is designed to generate the steering torque control commands for the USV. To further enhance the tracking performance of the system, we introduce a non-singular terminal integral sliding mode surface with a double power convergence law and redesign the backstepping sliding mode controller for the USV heading control. Meanwhile, to circumvent the differential explosion issue in traditional backstepping control, we simplify the controller design by utilizing a second-order sliding mode filter to accurately estimate the differential signals of the virtual control quantities. Theoretical analysis and simulation results demonstrate that the proposed control algorithm improves the convergence speed, adaptive ability, and anti-interference ability in complex environments compared to traditional linear backstepping sliding mode control, thereby enhancing its engineering practicability. This research offers a more efficient and reliable method for precise heading control and path tracking of USVs in complex and dynamic environments.

This paper examines the control challenges faced by underactuated Autonomous Underwater Vehicles (AUVs) under ocean current disturbances. It proposes a Backstepping Integral Sliding Mode Control (BISMC) strategy to enhance their adaptability and robustness. The BISMC strategy integrates the system decomposition capability of the backstepping control method with the rapid response and robustness advantages of the Sliding Mode Control method, enabling the design of a heading controller and a double closed-loop depth controller. By introducing an integral component, the strategy eliminates steady-state errors caused by ocean currents, accelerating system convergence and improving accuracy. Furthermore, a saturation function is employed to mitigate output chattering issues. Simulation results demonstrate that the BISMC controller significantly enhances the control precision and anti-disturbance capabilities of AUVs under low-frequency ocean current disturbances, showcasing exceptional adaptive and self-disturbance rejection performance.