# Adaptive Neural Network Control of Zero-Speed Vessel Fin Stabilizer Based on Command Filter
## 1 Introduction  
Vessels in navigation operations may be easily disturbed by harsh environmental factors such as wind, waves, currents, etc., and violent rolling motions may threaten the life and safety of the vessel itself, which also may cause capsizing or other major accidents of vessel destruction and death [1]. In this context, scholars of the ocean engineering community have proposed many effective anti-rolling methods, such as installing bilge levels [2], using a rudder for stabilization [3], adding an anti-rolling tank [4], installing anti-rolling fins [5], etc. The works [6, 7] pointed out that a bilge keel can reduce the roll angle of the vessel by about 20%, an anti-rolling tank can reduce the roll by up to 50%, and a rudder can reduce the roll by about 60%. In contrast, a fin stabilizer has the best anti-roll effect, which can reach about 85-90%. Therefore, many scholars have devoted their attention to fin stabilizers and proposed a variety of different control methods [8]. For the control issue of fin stabilizer, in the early stage, PID control based on [PERSON]'s linear model [9] has a good anti-rolling effect for small-angle vessel rolling, and has been widely used. When the ship rolls at a large angle, the nonlinear characteristic of model parameters is inspired. However, the traditional PID control strategy is designed based on the [PERSON] linear model, which cannot have effective system nonlinear characteristics, so it is no longer applicable. To this end, scholars have introduced nonlinear control technology methods into the fin stabilizer control of vessel roll and proposed a series of control methods, such as sliding mode control [10, 11], model predictive control [12], the Lyapunov direct method [13], and adaptive backstepping control [14]. In addition, the vessel rolling control system also needs to consider the uncertainties and actuator saturation. In view of the uncertainty of vessel rolling control systems, [15] used the fuzzy logic system to approximate the system uncertain parts and proposed a robust adaptive fuzzy controlscheme for vessel roll stabilization. In [16], a variable structure robust fin control scheme was proposed for vessel roll stabilization. In recent years, neural networks have been widely used in the control of nonlinear systems due to their good nonlinear approximation ability and self-learning ability. This neural network-based control strategy also plays an important role in the vessel's roll stabilization control. In [17], an adaptive control scheme based on a neural network and an adaptive backstepping method was proposed to overcome the uncertainties of the rolling control system. In [18], an RBF neural network is used to estimate the uncertainty, and a new type of fin stabilizer lift feedback adaptive control system is designed which effectively improves the anti-roll effect. In [19], an adaptive PID controller based on a BP neural network is designed. Through the prediction output of vessel roll angle, the self-tuning of PID controller parameters is realized by using the adaptive and nonlinear characteristics of a neural network. In [20], the combination of a wavelet neural network and the adaptive control design of a vessel fin stabilizer system effectively improved the shortcomings of the poor adaptability of conventional PID control, and the control system was shown to have good fault tolerance and strong nonlinear adaptability. Regarding the external uncertainty of the system, it is estimated by introducing a disturbance observer in [21; 22; 23; 24]. Because of its unique advantages, the disturbance observer technique has also received much attention from scholars [25; 26; 27]. Another practical problem regarding the fin stabilizer equipped on vessels is of the physical constraint, i.e., input saturation, which is inevitable [28].