In this article, based on partial differential equations (PDEs), the flexible manipulator system with both dead-zone input and state constraints is studied. The dynamic model of the flexible manipulator system is described by PDEs. The parameters of the dead-zone input are unknown, and the state constraint problem is also considered. An adaptive approach is proposed to offset the effects caused by dead-zone input. Thus, to guarantee that all states remain within their respective constraint regions, the boundary control law based on the barrier Lyapunov function is given, and an adaptive controller is designed. According to the Lyapunov analysis method, the control method is given to ensure that all signals of the closed-loop system are bounded and all states satisfy the constraint conditions. Finally, simulation results show the effectiveness of the proposed control method in this article.

中文翻译：

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带有死区输入的偏微分方程建模的柔性机械臂系统自适应约束控制

在本文中，基于偏微分方程（PDE），研究了具有死区输入和状态约束的柔性机械臂系统。柔性机械手系统的动力学模型由偏微分方程描述。死区输入参数未知，还考虑了状态约束问题。提出了一种自适应方法来抵消死区输入造成的影响。因此，为了保证所有状态都保持在各自的约束范围内，给出了基于势垒Lyapunov函数的边界控制律，并设计了自适应控制器。根据李雅普诺夫分析方法，给出控制方法，以保证闭环系统的所有信号都是有界的，并且所有状态都满足约束条件。最后，