With the more extensive application of flexible robots, the expectation for flexible manipulators is also increasing rapidly. However, the fast convergence will cause the increase of vibration amplitude to some extent, and it is difficult to obtain vibration suppression and satisfactory transient performance at the same time. In order to deal with the problem, a fixed-time learning control method is proposed to realize the fast convergence. The constraint on system outputs, system uncertainty, and input saturation is addressed under the fixed-time convergence framework. A novel adaptive law for neural networks is integrated into the backstepping method, which enhances the learning rate of neural networks. The imposed constraint on the vibration amplitude is guaranteed by using the barrier Lyapunov function (BLF). Moreover, the chattering problem is addressed by approximating the sign function smoothly. In the end, some simulations have been carried out to show the effectiveness of the proposed method.

中文翻译：

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具有固定时间收敛性的约束两连杆柔性机器人机械手的振动控制。

随着柔性机器人的应用越来越广泛，人们对柔性机械手的期望也越来越高。但是，快速收敛会在一定程度上引起振动幅度的增加，难以同时获得振动抑制和满意的暂态性能。针对该问题，提出了一种固定时间学习控制方法来实现快速收敛。在固定时间收敛框架下解决了对系统输出、系统不确定性和输入饱和的约束。一种新的神经网络自适应律被集成到反推法中，提高了神经网络的学习率。通过使用障碍李雅普诺夫函数 (BLF) 来保证对振动幅度施加的约束。而且，通过平滑地逼近符号函数来解决颤振问题。最后，进行了一些仿真，证明了所提方法的有效性。