Recently, a first-order differentiator based on time-varying gains was introduced in the literature, in its nonrecursive form, for signals having a second-order derivative bounded by a known time-varying function, where such time-varying bound has a logarithmic derivative bounded by a known constant. It has been shown that such differentiator is globally finite-time convergent. In this article, we redesign such an algorithm, using time base generators (a class of time-varying gains), to obtain a differentiator algorithm for the same class of signals, but with guaranteed convergence before a desired time, that is, with fixed-time convergence with an a priori user-defined upper bound for the settling time. Thus, our approach can be applied for scenarios under time-constraints. We present numerical examples exposing the contribution with respect to related state-of-the-art algorithms.

中文翻译：

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基于时变增益的预定义时间一阶精确微分器

最近，文献中引入了基于时变增益的一阶微分器，以其非递归形式，用于具有以已知时变函数为界的二阶导数的信号，其中这种时变界具有对数以已知常数为界的导数。已经表明，这种微分器是全局有限时间收敛的。在本文中，我们重新设计了这样一种算法，使用时基生成器（一类时变增益），以获得同一类信号的微分算法，但在所需时间之前保证收敛，即具有固定- 时间收敛与先验用户定义的建立时间上限。因此，我们的方法可以应用于时间限制下的场景。