# Notes-Global uniform asymptotic stabiliztion of an underactuated surface vessel

Feb 28, 2019

- 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

where

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.

1 | @inproceedings{mazenc2002global, |