An adaptive finite-time filtered backstepping sliding mode controller is designed to solve the rudder roll stabilization control problem of underactuated ships in unknown wave disturbance conditions.

First, in order to avoid differential operation for the virtual control law, a first-order filter is introduced to address the problem of differential explosion that affects the backstepping approach. By combining the filtered backstepping technique with adaptive sliding mode control, finite-time convergent control laws for rudder roll stabilization are designed on the basis of the finite-time control theory. Finally, the stability of the heading control subsystem and roll damping subsystem is proven by the Lyapunov stability theory.

The simulation results indicate that the designed controller can realize course tracking and roll damping simultaneously in finite time under different wave disturbance conditions. Compared with backstepping sliding mode control, the designed controller can improve the course-keeping control performance, and the roll reduction rate is increased by 5%.

The proposed method can provide useful references for the rudder roll stabilization control problem of underactuated ships.