Objectives  This paper investigates the distributed time-varying formation control of a swarm of under-actuated Unmanned Surface vehicles （USVs） guided by multiple leaders in the presence of complex model uncertainties and unknown ocean disturbances.

  Methods  At the kinematic level, distributed time-varying formation guidance laws are designed on the basis of the containment method and path maneuvering principle; at the kinetic level, the surge speed and yaw rate control laws are developed on the basis of the Extended State Observer (ESO) method such that the influences of the model uncertainties and unknown disturbances are mitigated. Further, cascade system stability analysis is undertaken, and the validity of the controller is demonstrated via a simulation.

  Results  It shows that the closed-loop distributed time-varying formation control system for USV is input-to-state stable by the cascade system stability theory. The simulation results verify the effectiveness of the control method.

  Conclusions  With the proposed controller, USVs are able to achieve the predefined time-varying formation while following the convex combination of multiple leaders.