Semi-global practical stabilization and disturbance adaptation for an underactuated ship

We consider the problem of stabilizing the position and orientation of a sh ip to constant desired values, when the ship has only two independent contr ols and also the ship is subject to an environmental force of unknown magni tude. We propose a time-varying feedback control law and a disturbance adap tation law, and show that this provides semi-global practical asymptotic st ability. The control and adaptation laws are derived using a combined integ rator backstepping and averaging approach. Simulation results are presented .