## 1 Introduction
To prevent output constraint violation, a symmetric BLF was employed in [25] and trajectory tracking with output constraints was realized. A two layered optimal approach towards cooperative motion planning of a USV in a constrained maritime environment was proposed in [26]. Reference [27] integrated the modules of efficient optimal path planning, robust path following guidance and the cooperative swarm aggregation approach towards development of a new hybrid framework for cooperative navigation of swarm of USVs to enable optimal and autonomous operation in a maritime environment. Moreover, the information exchange between vehicles is a challenging problem. Most of the current research assumes that the full states of the leader can be accessed by the follower. The adaptive finite-time decentralized control problem was addressed in [28] with the time-varying output-constraint. Under the consideration of input quantization and dynamic uncertainties, a decentralized adaptive NN PI tracking control was developed for the interconnected nonlinear system in [29]. A new estimate-based dynamic event-triggered output feedback control for networked control systems subjected to nonlinear uncertainties was proposed in [30]. The BLF was used to solve the problem of state constraints for USV and the input saturation was considered in [31]. All the references listed need the full-state information of the leader or the desired trajectory. Actually, due to the reason of economy or efficiency for the formation control problem, only the position and heading can be obtained by the follower and the velocity information is unavailable. This implies that a practical control method which is less demanding for communications should be developed. A fuzzy state observer was introduced to estimate the unmeasurable state variables in [32]. An event-triggered \(H\infty\) tracking control was first established for nonlinear NCSs in [33], which leads to a considerable reduction of sending data from the controller to the ROV. Unlike the existing studies in the previous literature, where the full states need to be known, this paper addresses the problem of the unavailability of the leader's velocity to the follower, which is more practical in modern applications. The value of BLF will increase to infinity when its arguments are close to some specified value. So, keeping the BLF bounded could ensure that the constraints are never violated in the closed-loopsystem. Motivated by the above research and the property of BLF, a model-based formation control under the consideration of collision avoidance and effective communication distance constraints is proposed for USV, different from [6,24]. In this paper, the errors combined with a BLF are directly used to design the formation control instead of complex error conversion through the guaranteed performance function, which reduces the amount of calculation and simplifies the design of the control. Compared to existing work in this field, the main contributions of this paper are threefold. * A BLF is used to tackle the problem of multiple USV constraints ensuring that the satisfactory formation performance with collision avoidance distance and connectivity constraints are never violated during the whole operation. * An adaptive NN control combined with a symmetric BLF is developed for autonomous USV to deal with the unmodeled dynamics and parameter uncertainties caused by hydrodynamic damping terms. * Unlike the existing studies in the previous literature, where the full states need to be known, this paper addresses the problem of the unavailability of the leader's velocity to the follower using a reconstruction module, which is more practical in modern applications. One of the contributions thus lies in that this method can accurately reconstruct the target velocity in finite time. This paper is organized as follows. Section 2 introduces the preliminaries and problem description. Section 3 is devoted to model-based BLF control and NN adaptive control for multiple USV.