一种基于时变增益的预定时间一阶精确微分器
A predefined-time first-order exact differentiator based on time-varying gains
摘要：
最近，在文献中引入了基于时变增益的一阶微分器，其非递归形式，用于一类可微信号$y(t)$，满足$|\ddot{y}(t)|\leq L(t-t_0)$，对于已知函数$L(t-t_0)$，使得$\frac{1}{L(t-t_0)}\left|\frac{d {L}(t-t_0)}{dt}\right|\leq M$具有已知常数$M$。它已被证明，这样的微分器是全球有限时间收敛。在本文中，我们重新设计了这样的算法，使用时基生成器（一类时变增益），以获得用于同一类信号的微分器算法，并保证在期望的时间之前收敛，即，具有固定时间收敛，并具有先验用户定义的建立时间的上界。因此，我们的方法可以应用于在时间限制的情况下。我们提出的数值例子，暴露的贡献相对于国家的最先进的算法。
英文摘要：
Recently, a first-order differentiator based on time-varying gains was introduced in the literature, in its non recursive form, for a class of differentiable signals $y(t)$, satisfying $|\ddot{y}(t)|\leq L(t-t_0)$, for a known function $L(t-t_0)$, such that $\frac{1}{L(t-t_0)}\left|\frac{d {L}(t-t_0)}{dt}\right|\leq M$ with a known constant $M$. It has been shown that such differentiator is globally finite-time convergent. In this paper, 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, with guaranteed convergence before a desired time, i.e., 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 state-of-the-art algorithms.
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