Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation

Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation

Recent force-fatigue mathematical models in biomechanics [7] allow to predict the muscular force response to functional electrical stimulation (FES) and leads to the optimal control problem of maximizing the force. The stimulations are Dirac pulses and the control parameters are the pulses amplitude...

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Main Authors: Bakir Toufik, Bonnard Bernard, Bourdin Loïc, Rouot Jérémy
Format: Article
Language:English
Published: EDP Sciences 2021-08-01
Series:ESAIM: Proceedings and Surveys
Online Access:https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107101.pdf
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spelling doaj-7b8e1131ab4545c791fca9aa27ec06d02021-09-02T09:29:22ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592021-08-017111010.1051/proc/202171101proc2107101Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulationBakir Toufik0Bonnard Bernard1Bourdin Loïc2Rouot JérémyUniv. Bourgogne Franche-Comté, ImViA LaboratoryUniv. Bourgogne Franche-Comté, IMB Laboratory UMR CNRSXLIM Research Institute, UMR CNRS 7252, University of LimogesRecent force-fatigue mathematical models in biomechanics [7] allow to predict the muscular force response to functional electrical stimulation (FES) and leads to the optimal control problem of maximizing the force. The stimulations are Dirac pulses and the control parameters are the pulses amplitudes and times of application, the number of pulses is physically limited and the model leads to a sampled data control problem. The aim of this article is to present and compare two methods. The first method is a direct optimization scheme where a further refined numerical discretization is applied on the dynamics. The second method is an indirect scheme: first-order Pontryagin type necessary conditions are derived and used to compute the optimal sampling times.https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107101.pdf
collection DOAJ
language English
format Article
sources DOAJ
author Bakir Toufik
Bonnard Bernard
Bourdin Loïc
Rouot Jérémy
spellingShingle Bakir Toufik
Bonnard Bernard
Bourdin Loïc
Rouot Jérémy
Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
ESAIM: Proceedings and Surveys
author_facet Bakir Toufik
Bonnard Bernard
Bourdin Loïc
Rouot Jérémy
author_sort Bakir Toufik
title Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
title_short Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
title_full Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
title_fullStr Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
title_full_unstemmed Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
title_sort direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
publisher EDP Sciences
series ESAIM: Proceedings and Surveys
issn 2267-3059
publishDate 2021-08-01
description Recent force-fatigue mathematical models in biomechanics [7] allow to predict the muscular force response to functional electrical stimulation (FES) and leads to the optimal control problem of maximizing the force. The stimulations are Dirac pulses and the control parameters are the pulses amplitudes and times of application, the number of pulses is physically limited and the model leads to a sampled data control problem. The aim of this article is to present and compare two methods. The first method is a direct optimization scheme where a further refined numerical discretization is applied on the dynamics. The second method is an indirect scheme: first-order Pontryagin type necessary conditions are derived and used to compute the optimal sampling times.
url https://www.esaim-proc.org/articles/proc/pdf/2021/02/proc2107101.pdf
work_keys_str_mv AT bakirtoufik directandindirectmethodstooptimizethemuscularforceresponsetoapulsetrainofelectricalstimulation
AT bonnardbernard directandindirectmethodstooptimizethemuscularforceresponsetoapulsetrainofelectricalstimulation
AT bourdinloic directandindirectmethodstooptimizethemuscularforceresponsetoapulsetrainofelectricalstimulation
AT rouotjeremy directandindirectmethodstooptimizethemuscularforceresponsetoapulsetrainofelectricalstimulation
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