Objective A finite-time disturbance observer-based optimal backstepping control (FDO-OBC) method is proposed for the issue of unknown disturbances and formation changes in the formation trajectory tracking of unmanned surface vehicles (USVs).

Methods First, the USV formation control framework is established on the basis of the virtual structure method, and the kinematics and dynamics formation controllers are designed. Second, a finite-time disturbance observer is introduced to estimate and compensate for unknown environmental disturbances in real time. Further, a dynamic trajectory optimization strategy based on optimal backstepping control is proposed for the trajectory tracking issue of formation change, and the information of the disturbance observer is used to calculate the optimal control input and achieve the dynamic optimization of USV formation trajectory tracking. Finally, Lyapunov stability theory is used to demonstrate the stability of the designed formation control method.

Results The simulation results indicate that the proposed control strategy can effectively improve the accuracy and robustness of the USV formation system.

Conclusion The FDO-OBC method provides a new technical means for the design of USV formation control systems under unknown environmental disturbances.