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In order to track the desired path under unknown parameters and environmental disturbances, an adaptive backstepping sliding mode control algorithm with a neural estimator is proposed for underactuated ships considering both ship-bank interaction effect and shift angle. Using the features of radial basis function neural network, which can approximate arbitrary function, the unknown parameters of the ship model and environmental disturbances are estimated. The trajectory tracking errors include stabilizing sway and surge velocities errors. Based on the Lyapunov stability theory, the tracking error will converge to zero and the system is asymptotically stable. The controlled trajectory is contractive and asymptotically tends to the desired position and attitude. The results show that compared with the basic sliding mode control algorithm, the overshoot of the adaptive backstepping sliding mode control with neural estimator is smaller and the regulation time of the system is shorter. The ship can adjust itself and quickly reach its desired position under disturbances. This shows that the designed RBF neural network observer can track both the mild level 3 sea state and the bad level 5 sea state, although the wave disturbance has relatively fast time-varying disturbance. The algorithm has good tracking performance and can realize the accurate estimation of wave disturbance, especially in bad sea conditions.

Adaptive Neural Backstepping Sliding Mode Heading Control for Underactuated Ships with Drift Angle and Ship-Bank Interaction