Notes-Global uniform asymptotic stabiliztion of an underactuated surface vessel
- This is a Time-varying Continuous Approach.
The dynamics of an underactuated ship is
The coordinate transformations
are first used to transform the ship system to
where and . Then the following nontrivial coordinate transformations
are applied to the transformed ship system to obtain the new system:
Let and be strictly positive constants such that . The control and are designed in the paper as
It is proven that the closed loop system is GAS at the origin in the paper.
Remark: The stabilizer design mentioned above is nontrivial, it is difficult to extend the control design scheme to solve a trajectory-tracking problem, and the convergence of the stabilizing errors to zero is slow. In addition, the physical meaning of feedback is not clear.