In this article, we investigate the stabilization control problem of a flexible marine riser system with a failed and bounded control action and time-varying boundary constraints. The considered system is modeled as a distributed parameter system dominated by a partial differential equation. The involved problems are extended to some more general conditions. The saturation and failures of the actuator make the input and output of the actuator a nonlinear relationship, which leads to the normally designed control input invalid. By applying the Nussbaum gain technique, we report a synthetical control method to tackle the input nonlinearity. A piecewise barrier Lyapunov function (BLF) is introduced to reduce the boundary displacement in an asymmetric open set. Compared with the traditional BLFs, the initial boundary displacement is not forced to retain within the given region by integrating a shifting function into the BLF design. In addition, the adaptive method is combined with the hyperbolic tangent function to provide a smooth control solution to the unknown parameters from nonlinear input and external perturbation. Relying on a Lyapunov-based analysis and a numerical simulation, it is proven that the actuated riser system is uniformly bounded and the boundary displacement always keeps in the limited set even subject to actuator failures and limitations.

中文翻译：

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具有失效和有界致动器和时变边界约束的柔性海洋立管的稳定控制

在本文中，我们研究了具有失效和有界控制动作和时变边界约束的柔性海洋立管系统的稳定控制问题。所考虑的系统被建模为由偏微分方程支配的分布式参数系统。所涉及的问题扩展到一些更一般的条件。执行器的饱和和失效使执行器的输入和输出呈非线性关系，导致正常设计的控制输入无效。通过应用 Nussbaum 增益技术，我们报告了一种解决输入非线性的综合控制方法。引入分段势垒李雅普诺夫函数 (BLF) 以减少非对称开集中的边界位移。与传统的 BLF 相比，通过将移位函数集成到 BLF 设计中，不会迫使初始边界位移保持在给定区域内。此外，自适应方法与双曲正切函数相结合，为来自非线性输入和外部扰动的未知参数提供平滑的控制解决方案。依靠基于李雅普诺夫的分析和数值模拟，证明了驱动立管系统是均匀有界的，即使受到驱动器故障和限制，边界位移也始终保持在有限集内。