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Synthesis on a class of algebraic differentiators and application to nonlinear observation

Da-Yan Liu 1 Olivier Gibaru 2, 3 Wilfrid Perruquetti 2, 4, 5
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The recent algebraic parametric method proposed by Fliess and Sira-Ramirez has been extended to numerical differentiation problem in noisy environment. The obtained algebraic differentiators are non-asymptotic and robust against corrupting noises. Among these algebraic differentiators, the Jacobi differentiators has been used in many applications. In this paper, we summarize some existing error analysis results to give a strategy on how to chose the design parameters for the Jacobi differentiators. Then, we provide new algorithms which are more robust against the numerical errors produced with negative design parameters' values. Finally, we consider an application to nonlinear observation, where we compare the Jacobi differentiators to the high gain observer and the high order sliding modes differentiator.
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https://hal.inria.fr/hal-00986345
Contributor : Dayan Liu <>
Submitted on : Friday, May 2, 2014 - 11:14:10 AM
Last modification on : Saturday, October 3, 2020 - 3:20:00 AM
Long-term archiving on: : Saturday, August 2, 2014 - 11:45:10 AM

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Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti. Synthesis on a class of algebraic differentiators and application to nonlinear observation. The 33rd Chinese Control Conference (CCC), Jul 2014, Nanjing, China. ⟨hal-00986345⟩

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