Transverse Function Control for Underactuated MSV With Stochastic Disturbances Under Output Error Constraints

This paper investigates the trajectory tracking control problem of an underactuated marine surface vehicle (MSV) with stochastic disturbances, where the tracking errors are required to preserve within the predefined constraint bounds. Since the vehicle system is exposed to the environmental stochastic disturbances, the difficulty arisen from Hessian terms induced by stochastic differentiation rule is overcome by introducing a quartic Lyapunov function. To tackle the difficulties caused by underactuation and nonzero off-diagonal terms in the system matrix, we develop a transverse function control approach to introduce an additional control input in backstepping procedure. A tan-type barrier Lyapunov function is introduced to guarantee the satisfaction of the prescribed tracking error constraints. Based on backstepping procedure, barrier Lyapunov function, transverse function control approach, and Lyapunov synthesis, feedback control laws are proposed to ensure that the tracking errors converge exponentially to a small neighborhood of zero, and the constraint requirements on the tracking errors are not violated in the course of operation in probability despite the presence of stochastic disturbances. Simulation results illustrate the performance of the proposed tracking control.