This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov–Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.

中文翻译：

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通过双时变增益方法对时滞非线性系统进行自适应规定时间控制

本文研究一类参数不确定的时滞非线性系统的全局规定时间镇定问题。首先，我们设计了两种具有特殊性质的时变增益，其中一种被引入虚拟控制器中以实现规定时间收敛，另一种用于构造Lyapunov-Krasovskii（LK）泛函和Lyapunov函数来处理非线性分别为时滞项和未知参数。然后，利用双时变增益和无标度反步设计方法，构建动态状态反馈控制器，保证在规定时间内所有状态变量达到零，并且规定时间可以提前指定。然后，基于新泛函和正则微分不等式，我们给出了所有变量上界的显式表达式，这对于证明所有系统变量的有界性起到了重要作用。最后，给出了一个仿真例子来证明该方法的有效性。