This paper studies the problem of finite-time consensus (FTC) for uncertain multiple mechanical systems with unknown backlash nonlinearity and external disturbance. Combining finite-time control technique and graph theory, a distributed adaptive FTC protocol is proposed. Radial basis function neural networks are employed to approximate the unknown functions. If the designed parameters of control algorithms and adaptive laws are appropriately chosen, then it can be proved that the position errors between arbitrary two mechanical systems will converge to a small region of zero in finite time as well as the velocity errors. Finally, the effectiveness of the proposed control scheme is verified by numerical simulation.

中文翻译：

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具有未知反向间隙非线性和不确定动力学的多个机械系统的自适应有限时间一致性

本文研究了具有未知背隙非线性和外部干扰的不确定多机械系统的有限时间一致性（FTC）问题。结合有限时间控制技术和图论，提出了一种分布式自适应FTC协议。采用径向基函数神经网络来逼近未知函数。如果适当地选择了控制算法和自适应定律的设计参数，则可以证明任意两个机械系统之间的位置误差将在有限时间以及速度误差中会聚到零的小区域。最后，通过数值模拟验证了所提出的控制方案的有效性。