Robust Stabilization Control of Underactuated Surface Vessels with Current Disturbances

This paper investigates the stabilization control problem of underactuated surface vessels which suffers from unknown ocean current and has non-diagonal system matrices. Firstly, a nonlinear observer is constructed to measure the value of ocean current. Then, a novel output is designed ensuring that the relative degree of system is well-defined. Different from the traditional hand-like position output that only yields bounded stability, the proposed output includes a new term and helps to obtain asymptotic stability. After designing output, the input-output feedback linearization approach, the cascaded system theory and the observer are applied to design a robust control law, steering the output and its derivative to zero asymptotically, regardless of the unknown current. Zero dynamics equation is calculated and analyzed, showing that for zero output and zero estimation errors, the vessel will regulate its orientation to be the same as current direction, and its yaw velocity will tend to zero. This leads to that the position asymptotically converges to desired position, the surge velocity approaches the minus value of current velocity, and the sway velocity goes to zero. A simulation example is presented to demonstrate the effectiveness of the proposed control strategy.