## 1 Introduction  
In recent years, the application of unmanned underwater vehicles (UUVs) has grown steadily. Several activities related to the offshore industry, such as oceanic surveillance, undersea oil detections, seabed explorations, and so on, have been performed by using a group of low-cost, unmanned, small underwater vehicles. Its advantages are it is an effective, economic, and efficient solution, compared to a single expensive underwater vehicle. An essential topic in the cooperative control of multi-UUVs is the formation tracking problem [1; 2; 3]. It requires that all the UUVs reach into a formation with a desired shape from an arbitrary initial pose while the centroid of formation tracks a reference trajectory. According to [1], there are four main approaches, such as leader-follower approach, behavior-based approach, artificial potential approach, and virtual structure approach, to achieve the formation tracking problem. Moreover, the formation tracking problems for a group of multi-agent systems with nonlinear dynamics and external disturbances have been studied in [1; 3; 4; 5; 6; 7; 8]. In [1],the robust distributed formation design for multiple UUVs is presented, where the dynamics of underwater vehicles, which is subject to nonlinearity, parametric uncertainties, and external disturbances, are analyzed by combining the feedback linearization method and the robust compensation theory. Distributed formation tracking control and learning/identification of nonlinear uncertain AUV dynamics by using two-layer, namely, an upper-layer distributed adaptive observer and a lower-layer decentralized deterministic learning controller, is introduced in [3]. This article also addresses some very interesting issues, such as heterogeneous nonlinear uncertain dynamics, local information, and formation control performance. In [4; 9], a multi-layer neural network and an adaptive robust controller were developed to overcome unmodeled dynamics of under-actuated autonomous underwater vehicles and external disturbances with the prescribed performance. In addition, in [6], the trajectory tracking problem for a fully actuated autonomous underwater vehicle (AUV) that moves in the horizontal plane was developed. By using two neural networks, the long-time performance of a design control and the unknown dynamics are evaluated and compensated, respectively. For the issues of local information, the MORPH project [10] also introduced a formation control of underwater vehicles, using either inter-vehicle relative position measurements or range-only measurements. In [8], the distributed consensus tracking control problem for multiple strict-feedback systems with unknown nonlinearities under a directed graph topology is presented. The neural network is used to approximate and compensate for unknown nonlinear terms, which aims to design a local consensus controller. In [11], the leader-following consensus problem for a class of second-order multi-agent systems with input quantized is studied. A novel adaptive dynamic quantizer that can effectively reduce quantization error, with dynamic quantization interval and limited quantization level, is proposed. Furthermore, there are also studies of the tracking control problem for a team of quad-rotors under directed switching topologies [12] and for multiple unmanned helicopters under finite-time conditions [13]. Alternatively, in [14], a distributed consensus-based formation control for nonholonomic wheeled mobile robots is studied. This article addresses the issue, namely, perfect velocity tracking, i.e., the actual control inputs of the robot are equal to the desired control inputs. By designing neural network torque controllers with on-line learning, the robust velocity tracking and the desired formation is achieved and guaranteed. In [15], the input quantization, actuator faults, and unknown nonlinear of a consensus tracking control of multi-agent systems are studied under directed communication topology.