This paper investigates the synchronization control problem for supply and supplied ships during underway replenishment in a constantly time-varying ocean environment while considering the ocean environmental disturbances induced by wind, waves and currents, and the interaction effects between ships and their soft connections. It then proposes an event-triggered synchronization anti-disturbance control method based on disturbance estimation and compensation.

The first-order Markov process is used to describe the ocean environmental disturbances induced by waves, wind and currents that affect the supply ship, as well as the unmodeled dynamics. The interaction effects between the ships and their soft connections are included in the unmodeled dynamics. The online disturbance observer estimates time-varying unknown bounded disturbances which are compensated for in the control design using disturbance estimates. The auxiliary dynamic system helps to reduce the control saturation effects on anti-disturbance control. The event-triggered mechanism reduces the execution frequencies of control signals to avoid the excessive wear of the thrusters.

A simulation of a supply ship using the event-triggered control method shows the existence of a minimum sampling interval greater than 0 and the inability to trigger infinitely in a finite time. The controller can achieve synchronous navigation between supply and supplied ships while ensuring the global uniform ultimate boundedness of all closed-loop control signals.

The simulation results validate the effectiveness of the proposed event-triggered disturbance estimation and compensation control method.