## 1 Introduction
By contrast, sliding mode differentiators possess robustness to measurement noises [20]. In the context of motion control for AUVs, several output feedback control schemes have been proposed since the beginning of this century. In [21], the design and experimental results of a novel output feedback controller for slender-body underwater vehicles is proposed, with the velocity estimation achieved by using Luenberger observer. In [22; 23], nonlinear observers are designed for velocity estimation. In [24], an adaptive output feedback controller based on dynamic recurrent fuzzy neural network observer is proposed. In [16], a finite-time-convergent observer is developed to solve the estimation problem of the translational velocities. Hitherto, in the context of AUV output feedback control, the results of using differentiators to estimate velocity signals are very few. Real application systems usually operate under various constraints and restrictions arising from physical limitations or performance needs. Since this century, arising from the sustained research interest in the control field, a lot of results involving system constraints have been reported. These results promote the development of related technologies. Typical approaches of the class consist of model predictive control [25], reference governor [26] and barrier Lyapunov function [27]. In recent years, the design of state/output-constrained  
Figure 1: Six DOFs motions of AUVs. controllers based on barrier Lyapunov function has attracted great attention [28; 29; 30]. In the context of adaptive control design for AUVs, the number of relevant literature results is very limited [31]. The adaptive control design for AUVs with system constraints, as well as to meet the requirement of output feedback, is still a subject worthy of further study. Motivated by the above discussion, this work investigates the output feedback adaptive control method for AUVs with deferred output constraint. The main contributions of this work can be summarized as follows:  
1. The deferred output constraint in adaptive control design is implemented by constructing the auxiliary reference signal. Meanwhile, this construction is also beneficial to improve the smoothness of control input in the early stage of system operation. 2. Both the state feedback control scheme and output feedback control scheme are developed for AUVs with deferred output constraints. 3. By using the proposed control scheme, all the signals in closed loop are proved to be bounded, and better asymptotic tracking performance is achieved. PID algorithms are quite popular in industrial applications due to their simple algorithm and easy implementation. For the case that the derivative of output error is not measurable or cannot be accurately measured, PI control, as an alternative to PID control, is often adopted in the design of actual control system, which decreases the control accuracy. Moreover, the parameter tuning of PID control is not very easy. In PID control schemes, the demand of system constraint during system operation cannot be guaranteed. The remainder of this paper is organized as follows. The problem formulation and the preliminaries are given in Section 2. The construction of the auxiliary reference signal is introduced in Section 3. State feedback control design and output feedback control design are discussed in Section 4 and Section 5, respectively. In Section 6, the numerical simulation comparison is carried out to verify the effectiveness of the proposed adaptive control scheme. Finally, Section 7 concludes this work.