In this article, an observer‐based adaptive boundary iterative learning control law is developed for a class of two‐link rigid‐flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.

中文翻译：

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具有输入反冲和端点约束的刚柔机器人的基于扰动观察者的自适应边界迭代学习控制

在本文中，针对一类具有输入反冲，未知外部干扰和端点约束的两链刚性-柔性机械臂，开发了一种基于观察者的自适应边界迭代学习控制律。为了解决反冲非线性问题并确保振动抑制，在自适应边界控制设计中考虑了基于迭代学习概念的干扰观测器。障碍Lyapunov函数与边界控制定律结合在一起以限制端点状态。基于定义的势垒复合能量函数，可以保证刚性部件的跟踪角误差收敛，并通过严格的分析来抑制柔性部件的振动。最后，提供了数值模拟来说明所提出控制的有效性。