Pontryagin-Type Conditions for Optimal Muscular Force Response to Functional Electrical Stimulations

Toufik Bakir (), Bernard Bonnard (), Loïc Bourdin () and Jérémy Rouot ()
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Toufik Bakir: Univ. Bourgogne Franche-Comté, Le2i Laboratory EA 7508
Bernard Bonnard: Univ. Bourgogne Franche-Comté, IMB Laboratory UMR CNRS 5584
Loïc Bourdin: University of Limoges
Jérémy Rouot: ISEN Brest

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 14, 602 pages

Abstract: Abstract In biomechanics, recent mathematical models allow one to predict the muscular force response to functional electrical stimulations. The main concern of the present paper is to deal with the computation of optimized electrical pulses trains (for example in view of maximizing the final force response). Using the fact that functional electrical stimulations are modeled as Dirac pulses, our problem is rewritten as an optimal sampled-data control problem, where the control parameters are the pulses amplitudes and the pulses times. We establish the corresponding Pontryagin first-order necessary optimality conditions and we show how they can be used in view of numerical simulations.

Keywords: Functional electrical stimulation; Muscle mechanics; Optimal control problems; Sampled-data controls; Pontryagin-type necessary optimality conditions; 49K15; 93B07; 92B05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01599-4

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