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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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As important equipment in offshore engineering and freight transportation, shipboard cranes, working in non-inertial coordination systems, are complicated nonlinear systems with strong couplings and typical underactuation. To tackle the challenges in the controller design for shipboard boom cranes, which is a representative type of shipboard cranes, a comprehensive framework embedding moving horizon estimation (MHE) in model predictive control (MPC) is constructed in this paper while considering disturbances and noise. By utilizing MHE, velocity information can be estimated with high precision even though this is influenced by disturbances and measurement noises. This expected superiority can greatly ease the difficulties in directly measuring all states of shipboard boom cranes. Then, the estimated information can be passed to MPC to derive the optimal control law by solving a constrained optimal problem. During this process, the physical limits of shipboard boom cranes are fully considered. Therefore, the practicability of the proposed framework is highly suitable for the actual requirements of shipboard boom cranes. Finally, the framework is verified by designing three typical scenarios with different disturbances and/or noises. Comparisons with other control approaches are also performed to demonstrate the effectiveness.

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