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• A tan-type barrier Lyapunov function is introduced to ensure the prescribed performance of formation errors, the effectiveness of communication connections, and the avoidance of collisions. • A high-gain observer is designed to reconstruct the leader's velocity, which makes the control strategy more versatile in engineering applications. • An adaptive self-structuring neural network is proposed to compensate for model uncertainties and external disturbances, which can optimize the structure of the NNs by adjusting the number of neurons online, thus effectively reducing the computational burden. • A finite-time formation tracking controller for underactuated multiple USVs with error constraints is proposed to guarantee all signals of the closed-loop system to be practically finite-time stable. In this paper, a leader-follower formation control scheme of multiple underactuated surface vessels (USVs) is proposed for trajectory tracking, which not only solves the line of sight (LOS) and angle tracking errors within the prescribed performance, but also avoids collisions and maintains the communication connection distance. To achieve the prescribed performance and converge the tracking errors in finite time, a tan-type barrier Lyapunov function (TBLF) is introduced into the designed control strategy. In the process of formation control design, the measured values of the LOS range and angle are available, and the velocity of the leader is estimated using a high-gain observer. Next, a novel self-structuring neural network (SNN) is proposed to estimate the uncertain dynamics induced by the model uncertainties and environmental disturbances, and the computation amount is reduced by optimizing the number of neurons. Combining coordinate transformation and dynamic surface control (DSC), an adaptive NN controller with prescribed performance is proposed. The Lyapunov analysis shows that, although uncertain dynamics exist, the tracking errors can converge to a small region in finite time while achieving the prescribed performance, avoiding collisions, and maintaining the communication distance. In the closed-loop system, all signals are practical finite-time stable (PFS). Finally, the effectiveness of the proposed scheme is illustrated through a numerical simulation. [ABSTRACT FROM AUTHOR]