This paper studies the stabilization problem for the non-diagonal inertia and damping matrices underactuated unmanned surface vessels (USVs) in the presence of unknown time varying environment disturbances and state constraints. In this framework, we first convert the mathematical model into a form of two subsystems, which is easier amenable for stabilization, by applying several transformations. It is proved that the investigated problem can be reduced to one of the second subsystem. A novel time-varying state feedback control scheme based on backstepping method and prescribed Lyapunov function is proposed to ensure state constraints and guarantee the global stability of the reduced control system, as well as sufficient conditions to ensure controller feasibility are given. With adaptive neural networks (NNs), the controller can be easily extended to compensate uncertainty induced by unknown time-varying external disturbances (e.g., wind, waves, and currents). It is proved that all the states and stabilization functions in the overall closed-loop are globally uniformly bounded. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.
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