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Fixed-time convergent sliding-modes-based differentiators
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-09-11 , DOI: 10.1016/j.cnsns.2021.106033
Said Djennoune 1 , Maamar Bettayeb 2, 3 , Ubaid Muhsen Al-Saggaf 4, 5
Affiliation  

Conventional sliding-modes based differentiators make it possible to estimate successive derivatives of a given time-varying signal in finite-time and with exact convergence in noise free case. In general, the convergence time is an unbounded increasing function of initial estimation errors. Most already proposed solutions guarantee a convergence in a maximum time independent of initial conditions. In this paper, novel sliding mode differentiators with a prescribed convergence time are proposed. The convergence time can be chosen arbitrary whatever large initial estimation errors. The proposed key solution is based on a time-dependent transformation using modulating functions which make it possible to cancel the effect of initial conditions on the convergence time. New arbitrary order differentiators including the super-twisting algorithm based on modulating functions are introduced. Lyapunov functions and homogeneity tools are used to prove the convergence of the proposed first-order and arbitrary order differentiators, respectively. Robustness with respect to measurement noise is also addressed.



中文翻译:

基于固定时间收敛滑模的微分器

基于传统滑模的微分器可以在有限时间内估计给定时变信号的连续导数,并在无噪声情况下精确收敛。通常,收敛时间是初始估计误差的无界递增函数。大多数已经提出的解决方案保证在与初始条件无关的最长时间内收敛。在本文中,提出了具有规定收敛时间的新型滑模微分器。无论初始估计误差大,收敛时间都可以任意选择。所提出的关键解决方案基于使用调制函数的时间相关变换,从而可以消除初始条件对收敛时间的影响。引入了新的任意阶微分器,包括基于调制函数的超扭曲算法。Lyapunov 函数和同质性工具分别用于证明所提出的一阶和任意阶微分器的收敛性。还解决了关于测量噪声的稳健性问题。

更新日期:2021-09-23
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