In [39], a feed-forward multilayered architecture of artificial neural networks was proposed and applied to approximate the inverse model of the ship, which used a cost function to generate artificial neural network training data. In [40], a controller based on an artificial neural network was proposed for automatic ship docking. Furthermore, the structure of the artificial neural network was optimized by genetic algorithm. By generating reliable docking data, the simulation module of ship docking was established. In [41], a deep learning method was applied in the ship trajectory data restoration of an automatic identification system. By using bi-directional long short-term memory recurrent neural networks, when multiple points were missing, ship trajectories could be restored. In [42], a corrective system based on artificial neural networks was used for the coordinates of the ship's position and predicting ship trajectory. In [43], a deep neural network based on long-short-term-memory was proposed to identify a ship motion model and predict ship maneuvering motion. In [44], a course controller based on two-multilayered feed-forward neural network was proposed. The first neural network was used for the ship forward dynamic approximator, and the second neural network was used for the ship's course. In [47], a fuzzy PID control was applied to the ship's autopilot. In [48], three fuzzy controllers were proposed to ship berthing. The first one was used to control the longitudinal direction movement of ship toward to the normal of wharf by propeller. The second one was used to compute the relative bearing error with tugboat. The last one was designed for bringing the ship into wharf. In [49], a scheme based on observer-based adaptive fuzzy-output feedback was developed and applied for ship autopilot. In [50], to adjust the transient performance, a fuzzy logic system was proposed. In addition, a linear course-keeping controller based on second-order closed-loop gain shaping algorithm was designed. However, these methods are generally based on static networks; the network structure is first determined or the number of fuzzy rules is pre-given, then the modeling accuracy is evaluated using generalization errors and then directly used for ship motion control. Such algorithms inherently have large uncertainties and limitations due to the use of trial-and-error methods or relying on the knowledge of domain experts to determine structures or rules. Digital PID autopilot is a commonly used controller for ship course control. However, this automatic rudder is too sensitive for ship models and high-frequency disturbances, which leads to frequent steering, and it is difficult to achieve a good control effect [47]. With the development of control theory, fractional calculus theory [51] was used in controller design, resulting in a fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controller [52]. In 1999, [PERSON] first proposed a fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controller. The introduction of the integral order \(\lambda\) and the differential order \(\mu\) makes the controller have two more adjustable parameters, making the controller more flexible and robust. In [53], [PERSON] introduced the design and tuning methods of the fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controller, and software tools were also discussed. In [54], different types of variable-order fractional operators were defined and fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controllers for linear dynamical systems was designed. In [55], [PERSON] introduced fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controllers based on an opposition-based hunger games search algorithm, and applied it to a magnetic ball suspension system. In [56], a fractional-order PI\({}^{\lambda}\)D\({}^{\mu}\) controllers based on combination of Levy flight distribution and simulated annealing algorithms was applied for buck converters.