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This paper presents a course following control method for ships based on optimized backstepping (OB) technology. The backstepping technology is employed as the main control framework since the ship course can be modeled in the strict feedback form. Based on the actor-critic architecture and radial basis function (RBF) neural network (NN), the reinforcement learning (RL) strategy is introduced to avoid the difficulty in solving the traditional Hamilton-Jacobi-Bellman (HJB) equation directly. The actor NNs are used for carrying out the control law, while the critic NNs aim at evaluating the tracking performance. An auxiliary design system and Gaussian error function are employed to handle the practical problem of input saturation. The stability of the closed-loop system can be guaranteed via Lyapunov theory. Finally, simulation examples and comparison are provided to demonstrate and verify the superior performance and advantages on course following and energy saving of the control scheme proposed in this paper.INDEX TERMS Actor-critic architecture, Gaussian error function, input saturation, optimized backstepping, ship course following.

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