L2-Gain-Based Practical Stabilization of an Underactuated Surface Vessel

To obtain a stabilizer for an underactuated surface vessel with disturbances, an L2-gain design is proposed. Surge, sway, and yaw motions are considered in the dynamics of a surface ship. To ob-tain a robust adaptive controller, a diffeomorphism transformation and the Lyapunov function are employed in controller design. Two auxiliary controllers are introduced for an equivalent sys-tem after the diffeomorphism transformation. Different from the commonly used disturbance ob-server-based approach, the L2-gain design is used to suppress random uncertain disturbances in ship dynamics. To evaluate the controller performance in suppressing disturbances, two error sig-nals are defined in which the variables to be stabilized are incorporated. Both time-invariant dis-continuous and continuous feedback laws are proposed to obtain the control system. Stability analysis and simulation results demonstrate the validity of the controllers proposed. A comparison with a sliding mode controller is performed, and the results prove the advantage of the proposed controller in terms of faster convergence rate and chattering avoidance.

Automated summary

This study proposes a method to stabilize surge, sway, and yaw motions in surface ship dynamics, using L2-gain design to suppress random uncertain disturbances, and designing a robust adaptive controller through diffeomorphism transformation and Lyapunov function. Stability analysis and simulation results demonstrate the validity of the controllers proposed.