A novel nonlinear sliding mode control approach dealing with the formation control of under-actuated ships is presented in this paper. To avoid the singularity problem, state space of the system is partitioned into two regions, with one region bounded for terminal sliding mode control and its complement singular for that. And a linear auxiliary sliding mode controller is designed for system trajectories starting from the complement region. With the application of nonlinear sliding mode control approach and finite-time stability theory, a distributed controller is designed for individual under-actuated ship to achieve the given formation pattern within a finite time. Finally, two simulation examples are provided to verify the effectiveness and performance of the proposed approach.

中文翻译：

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使用非线性滑模控制的欠驱动船舶的有限时间编队控制


本文提出了一种新颖的非线性滑模控制方法，用于处理欠驱动船舶的编队控制。为了避免奇异性问题，系统的状态空间被划分为两个区域，其中一个区域用于终端滑模控制，其补奇异性用于该区域。并针对从补区开始的系统轨迹设计了线性辅助滑模控制器。应用非线性滑模控制方法和有限时间稳定性理论，为单个欠驱动船舶设计分布式控制器，使其在有限时间内实现给定的编队模式。最后，提供了两个仿真例子来验证所提出方法的有效性和性能。