Stabilization of USVs Under Mismatched Condition Based on Fixed-Time Observer

This study investigates the problem of asymptotic stabilization of underactuated surface vehicles (USVs) in the presence of simultaneous matched and mismatched disturbances. Within the framework of back-stepping control and by introducing a periodic term in the control laws of virtual yaw angle and surge velocity, a control design method is developed to stabilize the USVs into the bounded region. By the induction method, a novel fixed-time disturbance observer based on higher-order sliding mode differentiators are introduced. Then a control law based on the proposed observers is proposed, by which the errors between the virtual and actual yaw angle and surge velocity can converge to zero, and the state of the USVs converge to a bounded region. Numerical simulations are carried out to verify the proposed control schemes.