Trajectory tracking control for uncertain underactuated surface vessels with guaranteed prescribed performance under stochastic disturbances

The environmental disturbances acting on marine surface vessels are naturally stochastic. The control performance may be seriously deteriorated if the stochastic sea loads are ignored in control design. In this paper, the trajectory tracking control problem for uncertain underactuated surface vessels exposed to stochastic disturbances under prescribed performance constraints was addressed. By introducing a novel tan-type quartic barrier Lyapunov function (BLF) into the control design, such that (i) the Hessian terms induced by stochastic differentiation rule can be handled, and (ii) the prescribed transient and steady-state performance of tracking errors in probability can be guaranteed. To overcome the difficulties caused by underactuation and nonzero off-diagonal terms in system matrices, we develop a transverse function control method to introduce an additional controller. An important role of the design method is that it is not necessary to prove the stability of the sway dynamics separately in theory. Finally, simulation studies are carried out to validate the effectiveness of the proposed control protocol.