Stabilisation is an issue of great practical importance to the ship industry. This study considers the global asymptotic stability controller for a class of underactuated surface vessel possessing non-diagonal inertia and damping matrices. For the synthesis of controller, the investigated underactuated model is first converted into two cascade connected subsystems using input and state transformations. For these subsystems, it is shown that the stabilisation problem of this study can be reduced to the one of the second subsystem. By combining the method of adding a power integrator and the direct Lyapunov approach, a finite time switching control strategy is developed guaranteeing global asymptotic convergence of the full states to origin. The simulation results testify to the effectiveness of the presented control approach.

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This paper focuses on the tracking control problem for strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints. Time-varying asymmetric barrier Lyapunov functions are employed to ensure time-varying constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. High-order coupling terms caused by backstepping are cancelled through a novel variable substitution for the first time. Besides the normal case, where the full knowledge of the system is available, we also handle scenarios of parametric uncertainties. Asymptotic tracking is achieved without violation of any constraints, and all signals in the closed-loop system are ultimately bounded. State-constrained systems with input saturation and bounded disturbances are also considered; the tracking error converges to a bounded set around zero. The performance of the asymmetric-barrier-Lyapunov-function-based control is illustrated through a numerical example.