Objective  In order to solve the problems of most current ship formation control algorithms such as their long control cycle and poor timeliness, this paper proposes a finite-time control strategy based on an extended state observer (ESO).

  Methods  First, a nonlinear terminal sliding-mode control algorithm is proposed which overcomes the singularity problem of the traditional terminal sliding-mode by designing the control law in different regions. Then, the nonlinear terminal sliding-mode control and graph theory are then combined to realize finite-time ship formation control. In addition, the ESO is used to observe and compensate for the uncertainties and external disturbances in the ship model in order to ensure the accuracy of ship formation control. Finally, the Lyapunov theorem are used to verify the stability of the ship formation control law.

  Results  The simulation results show that the system error of the whole formation approaches zero in about five seconds using the proposed control strategy, thus its achieves stability.

  Conclusions  The proposed control strategy can effectively control ship formation and has fast control speed and good timeliness.