A discontinuous control method for dynamical positioning of underactuated surface vessels

For a second-order nonholonomic constraint exists in underactuated surface vessel system, which makes thesystem not meet the Brockett´s necessary condition, there is no continuously differentiable control law that can make the origin of the system asymptotically stable. After coordinate and feedback transformations, the stable feedback control laws are respectively proposed for two subsystems with finite-time control method, and then the dynamical positioning control problem is well solved by a discontinuous way. Results of computer simulation show the effectiveness of the proposed control method.