In this article, by utilizing the predefined-time stability theory, the predefined-time output tracking control problem for perturbed uncertain nonlinear systems with pure-feedback structure is addressed. The nonaffine structure of the original system is simplified as an affine form via the property of the mean value theorem. Furthermore, the design difficulty from the uncertain nonlinear function is overcome by the excellent approximation performance of RBF neural networks (NNs). An adaptive predefined-time controller is designed by introducing the finite-time differentiator which is used to decrease the computational complexity problem appeared in the traditional backstepping control. It is proved that the proposed control method guarantees all signals in the closed-loop system remain bound and the tracking error converges to zero within the predefined time. Based on the controller designed in this paper, the expected results can be obtained in predefined time, which can be illustrated by the simulation results.

中文翻译：

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受纯反馈形式和未知干扰影响的非线性系统的基于自适应微分器的预定义时间控制

本文利用预定义时间稳定性理论，研究了具有纯反馈结构的扰动不确定非线性系统的预定义时间输出跟踪控制问题。通过均值定理的性质，将原系统的非仿射结构简化为仿射形式。此外，RBF 神经网络 (NN) 的出色逼近性能克服了不确定非线性函数的设计难度。通过引入有限时间微分器设计了一种自适应预定义时间控制器，用于降低传统反步控制中出现的计算复杂度问题。证明所提出的控制方法可以保证闭环系统中的所有信号保持有界，并且跟踪误差在预定时间内收敛到零。基于本文设计的控制器，可以在预定的时间内获得预期的结果，仿真结果可以说明这一点。