This paper investigates how to design controllers to stabilize the underactuated surface vessel to desired constant location and orientation with vanishing velocities. The first control law is designed as a smooth function of position and orientation errors without using model parameters, where a gain is made time-varying to get over the nonholonomic constraint on model. Skew-symmetric and damping terms in model are exploited to help construct two particular Lyapunov functions, and Barbalat's lemma are combined to verify the global uniform asymptotic convergence of errors and velocities. Then, the second and the third control laws are devised as the forms of the first controller plus velocity feedbacks and can achieve the same stability as the first one but have a weaker gain condition. All the three controllers are robust to model parameters due to their absence in controllers and only require three model parameters' upper/lower bounds, decreasing the identification workload greatly. Moreover, they are the first smooth ones capable of achieving global uniform asymptotic full-state stabilization control of vessel with unknown model parameters. Effectiveness of the proposed controllers is demonstrated by numerical simulations.

中文翻译：

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模型参数未知的欠驱动水面舰艇全局均匀渐近稳定的鲁棒平滑控制

本文研究了如何设计控制器，以将欠驱动的水面舰艇稳定到所需的恒定位置和方向，并以消失的速度进行。第一个控制律被设计为位置和方向误差的平滑函数，不使用模型参数，其中增益随时间变化以克服模型的非完整约束。利用模型中的斜对称和阻尼项来帮助构建两个特定的 Lyapunov 函数，并结合 Barbalat 引理来验证误差和速度的全局一致渐近收敛。然后，将第二和第三控制律设计为第一控制器加速度反馈的形式，可以达到与第一控制器相同的稳定性，但增益条件较弱。三个控制器由于在控制器中的缺失而对模型参数具有鲁棒性，并且只需要三个模型参数的上/下界，大大减少了识别工作量。此外，它们是第一个能够实现具有未知模型参数的船舶的全局均匀渐近全状态稳定控制的平滑算法。数值模拟证明了所提出的控制器的有效性。