## 1 Introduction
### Related Works
It is shown that with the proposed method, the requirement for an error limit is never violated for all time. By using a non-linear disturbance observer, all uncertainties are estimated and compensated. The proposed track control can ensure that closed-loop system state is ultimately limited and final range can be arbitrarily small by arbitrary selection of parameters. The issue of controlling the maneuvering of sea surface vehicles by numerous virtual leaders, stating that movement is guided along with various path parameters, is examined in [28]. In addition, only a handful of sequential vehicles have access to the information of its virtual leaders. The problem of controlling the formation of a limited follower leader for a class of independent surface vessels with a range of line of sight (LOS) and angle constraints are considered in [29]. A new control structure ensures convergence into small areas arbitrarily in the zero range for a limited time for tracking errors, while the required constraints on the LOS range and angle are not violated. In the paper [30], the tracking path of the controller problem of a fully actuated surface vessel is limited to the asymmetric input and the output is addressed. An adaptive control approach is used barrier lyapunov function (BLF) and nussbaum function to implement trajectory tracking for a fully actuated surface vessel point under the asymmetric constraints of input and output. To adaptive an asymmetric saturation function, almost a tangent function is used in the form of smooth hyperbolic. The command system and auxiliary design system were adopted to avoid complex calculation, derived from virtual control and ensure its limitations. With the proposed approach, proved that tracking errors of the closed-loop system are ultimately limited. A controller for tracking path for a fully actuated surface vessel in the presence of output constraints and uncertainty using adaptive asymmetric barrier Lyapunov function (ABLF) and neural networks (NNs) [31; 32; 33]. This method proves that in the suggested proposal law, closed-loop system signals, threshold tracking are obtained, and output constraints are not violated too much. This paper [33] provides a way to exploit sea surface vessels with predicted tracking controls. By introducing an error function, the limited tracking control of the main vessel turned into the stability of an unrestricted system. Adaptive stability of the neural networks (NN) tracking control is designed for unspecified sea surface vessels. The proposed controller ensures that the output tracking errors of the system have transient preset and stable state control. In persistent excitation (PE) conditions, a NN adaptive controller is able to gain knowledge of the understanding, expression, and storage of the unknown system dynamics in the stable state control process. The neural controller was created usingthe stored knowledge, without the need to read the controller parameters, to achieve improved system control function. Controller for Ocean Surface Vessels is designed in [34] with accurate information about external impairments that operate on systems, that should be accurately estimated. To address this challenge, a new estimation approach was presented. The non-linear prediction rule was originally proposed. Under this rule, a sliding mode method is created based on the developed observer. The estimation error ensures to be stable in a limited time. Real disturbance can be estimated precisely with the error of zero estimate after a limited time. A quick and accurate estimate of the disruption is guaranteed. When vessels dynamic is also affected by the system's uncertainty, the proposed approach is able to estimate the total value of the uncertainty and disruptions simultaneously. An adaptive control for trajectory tracking autonomous underwater vehicle (AUV) using neural networks (NNs) in the discrete-time domain in [35]. A NN-based reinforcement learning algorithm is used to solve an unknown disorder, uncertainty, and non-linear input control.