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Abstract
The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuoustime and sampleddata settings. Fundamental performance limitations of causal differentiators, in terms of the smallest achievable worstcase differentiation error, are shown. A robust exact differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator exhibits a combination of properties that outperforms existing continuoustime differentiators: it is robust with respect to noise, it instantaneously converges to the exact derivative in the absence of noise, and it attains the smallest possible—hence optimal—upper bound on its differentiation error under noisy measurements. For samplebased differentiators, the concept of quasiexactness is introduced to classify differentiators that achieve the lowest possible worstcase error based on sampled measurements in the absence of noise. A straightforward samplebased implementation of the proposed linear adaptive continuoustime differentiator is shown to achieve quasiexactness after a single sampling step as well as a theoretically optimal differentiation error bound that, in addition, converges to the continuoustime optimal one as the sampling period becomes arbitrarily small. A numerical simulation illustrates the presented formal results.
Originalsprache  englisch 

Aufsatznummer  110725 
Seitenumfang  13 
Fachzeitschrift  Automatica 
Jahrgang  148 
DOIs  
Publikationsstatus  Veröffentlicht  Feb. 2023 
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Optimal Robust Exact Differentiation via Linear Adaptive Techniques
Richard Seeber (Redner/in)
24 Nov. 2021Aktivität: Vortrag oder Präsentation › Vortrag bei Workshop, Seminar oder Kurs › Science to science