Geodesic
Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation
Toufik Bakir1 ; Bernard Bonnard2 ; Loïc Bourdin3 ; Jérémy Rouot1, 2, 4, 3
1Univ. Bourgogne Franche-Comté, ImViA Laboratory EA 7535, Dijon, France
2Univ. Bourgogne Franche-Comté, IMB Laboratory UMR CNRS 5584, Dijon,
3XLIM Research Institute, UMR CNRS 7252, University of Limoges, Limoges, France
4and INRIA team Mc TAO, Sophia Antipolis, France
ESAIM. Proceedings, Tome 71 (2021), pp. 1-10
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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.
DOI : 10.1051/proc/202171101

Toufik Bakir  1   ; Bernard Bonnard  2   ; Loïc Bourdin  3   ; Jérémy Rouot  1 , 2 , 4 , 3

1 Univ. Bourgogne Franche-Comté, ImViA Laboratory EA 7535, Dijon, France
2 Univ. Bourgogne Franche-Comté, IMB Laboratory UMR CNRS 5584, Dijon,
3 XLIM Research Institute, UMR CNRS 7252, University of Limoges, Limoges, France
4 and INRIA team Mc TAO, Sophia Antipolis, France 
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     author = {Toufik Bakir and Bernard Bonnard and Lo{\"\i}c Bourdin and J\'er\'emy Rouot},
     title = {Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation},
     journal = {ESAIM. Proceedings},
     pages = {1--10},
     year = {2021},
     volume = {71},
     doi = {10.1051/proc/202171101},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202171101/}
}
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Toufik Bakir; Bernard Bonnard; Loïc Bourdin; Jérémy Rouot. Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation. ESAIM. Proceedings, Tome 71 (2021), pp. 1-10. doi: 10.1051/proc/202171101

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