# Adaptive Neural Network Control of Zero-Speed Vessel Fin Stabilizer Based on Command Filter
## 1 Introduction
In a vessel rolling control system, when the fin angle is used as the control input of the system, it may occur that the actual control input cannot reach the ideal control input level, which affects the stability of the control system [29]. Therefore, it is necessary to consider the influence of input saturation in the design process of vessel rolling control. To handle the effect of input saturation, refs [30; 31] used a gain-scheduling algorithm to deal with the input rate and amplitude saturation problem, which effectively improved the stability of vessel rolling control system. In [32], the adverse effect of input saturation on the adaptive capability of the system was effectively dealt with by designing an auxiliary dynamic system to correct the feedback error. For the issue of saturation constraint, there are several effective approaches, such as model augmentation [33], smooth function substitution [34], and augmented error signal (AES) [35]. Based on the above observations, this paper proposes a zero-speed vessel fin stabilizer adaptive neural network control strategy for the vessel rolling control problem in the presence of input saturation, dynamic uncertainty and external unknown disturbance. Firstly, an auxiliary dynamic system is constructed to prevent the adaptive capacity of the system from being destroyed by input saturation. Then, the neural network technology is employed to overcome the dynamic uncertainty of the system model, and the disturbance observer is used to estimate the external unknown disturbance. Considering that the model approximation ability of BP neural network is very dependent on learning samples and the convergence rate is slow, the number of hidden layer nodes of the wavelet neural network is difficult to determine. Furthermore, RBF neural networks have arbitrary approximation performance and optimal approximation performance in theory, and the learning convergence rate is fast; therefore, this paper selects an RBF neural network [6; 34; 36] to approximate the dynamic uncertainty of the system model. In addition, in engineering practice, due to the presence of high-frequency and low-frequency parts in the marine environment, the high-frequency parts may enter the vessel rolling motion control system. In this case, the roll angle caused by the high-frequency part will be polluted, and the backstepping method requires the derivative operation of the virtual control, which, in turn, will aggravate the adverse effects of the high-frequency part, making the control system unable to operate normally. Therefore, this research introduces command filtering technology in the design process to overcome the adverse effects of the high-frequency part of the ocean. The main contributions of this paper are as follows: (i) An auxiliary dynamic system (ADS) is designed to correct the feedback error to overcome the influence of input saturation on the adaptive ability of the system. (ii) A fusion of neural network technology and a nonlinear disturbance observer is designed for the dynamic uncertainty and external unknown disturbance of the vessel's roll control system, which not only breaks through the requirements of the disturbance observer for the knowledge of the controlled object model from the design mechanism but also overcomes the fact that the neural network technology cannot effectively reconstruct external disturbance. (iii) The introduction of a unique command filtering method which combines command filtering with the backstepping method overcomes the problem that the adverse effects of the high-frequency part of the ocean on the control system are aggravated by the backstepping method of the derivation operation. The purpose of this work is to reduce the vessel roll and achieve stabilization by the fin stabilizer for the zero-speed vessel, which is subject to unknown dynamic, ocean disturbance and input saturation. The work arrangement of this paper is as follows. Section 2 introduces the mathematical model and preliminary knowledge of vessel rolling motion.