Fixed-time convergent sliding-modes-based differentiators

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 al...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2022-01, Vol.104, p.106033, Article 106033
Main Authors: Djennoune, Said, Bettayeb, Maamar, Al-Saggaf, Ubaid Muhsen
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Differentiators
Errors
Estimating techniques
Fixed-time observers
Homogeneity
Initial conditions
Liapunov functions
Lyapunov functions
Mathematical functions
Modulating functions
Noise
Noise measurement
Sliding modes
Time dependence
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Summary: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. •Development of innovative sliding-modes-based arbitrary order differentiators.•The predefined convergence time is chosen whatever initial estimation errors.•Time dependant transformation is used to annihilate initial estimation errors.•Convergence is based on Lyapunov theory and homogeneity properties.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2021.106033