Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications

Othmane, Amine; Kiltz, Lothar; Rudolph, Joachim

doi:10.1080/00207721.2022.2025948

Cited by 20 publications

(23 citation statements)

References 167 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 3 See [Mboup et al(2009)] and [Othmane et al(2021), Othmane et al(2022)] for more details. Note also that estimating derivatives via integrals seems to have been first introduced by [Lanczos(1956)].…”

Section: Derivative Estimatementioning

confidence: 99%

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Mounier¹,

Join²,

Delaleau³

et al. 2023

Preprint

View full text Add to dashboard Cite

Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the "round trip time", i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as a "flat output." All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a function of the delay and its derivatives: they are frozen if the delay is kept constant. This flatness-like property, which demonstrates the mathematical discrepancy of the linear approximation adopted until today, yields also our control strategy in two steps: Firstly, designing an open-loop control, thanks to straightforward flatness-based control techniques, and secondly, closing the loop via Model-Free Control (MFC) in order to take into account severe model mismatches, like, here, the number of TCP sessions. Several convincing computer simulations, which are easily implementable, are presented and discussed.

show abstract

Section: Derivative Estimatementioning

confidence: 99%

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Mounier¹,

Join²,

Delaleau³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…can be approximated as low-pass filters of an arbitrary order, and the parameters can be computed from a desired cutoff frequency and the desired filter order. A summary of the tuning guidelines and their application on example case studies can be found in Othmane, Kiltz, and Rudolph (2022). An exhaustive list of applications including parameter estimation, state reconstruction, feedback control, fault diagnosis, anomaly detection, fault-tolerant control, and model-free control has been provided in Othmane et al (2022).…”

Section: Résumémentioning

confidence: 99%

“…A summary of the tuning guidelines and their application on example case studies can be found in Othmane, Kiltz, and Rudolph (2022). An exhaustive list of applications including parameter estimation, state reconstruction, feedback control, fault diagnosis, anomaly detection, fault-tolerant control, and model-free control has been provided in Othmane et al (2022). A MATLAB and Python toolbox implementing all necessary functions for the design, analysis, and discretisation of the filters has been released with the discussions in Othmane et al (2022) and is accessible in .…”

Section: Résumémentioning

confidence: 99%

“…The relations to existing methods such as deadbeat state estimation, Savitzky-Golay filters, Legendre filters, and mollification have been discussed in Kiltz (2017); Othmane et al (2022);…”

Section: Résumémentioning

confidence: 99%

“…These approaches and their implementation have been discussed in Ahmed et al (2016); Fliess, Join, and Mounier (2004); ; Kiltz, Join, Mboup, and Rudolph (2014); Deutscher (2020a, 2022); ; ; Tisserand, Lezama, Schweitzer, and Berviller (2015), for instance. An extensive list of applications in various domains is provided in Othmane et al (2022), for example.…”

Section: Numerous Approaches Have Been Developed For Fault Diagnosis ...mentioning

confidence: 99%

See 2 more Smart Citations

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Othmane

2023

At - Automatisierungstechnik

View full text Add to dashboard Cite

show abstract

Intelligent Control for Attenuating Vertical Vibrations in Vehicles

2023

Uncertainty and Artificial Intelligence

View full text Add to dashboard Cite

Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications

Cited by 20 publications

References 167 publications

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Active queue management for alleviating Internet congestion via a nonlinear differential equation with a variable delay

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

Intelligent Control for Attenuating Vertical Vibrations in Vehicles

Contact Info

Product

Resources

About