Indirect and Semi-direct Methods For Optimal Muscular Force Response to Functional Electrical Stimulation

Abstract : Recent force-fatigue mathematical models in biomechanics [5] allow to predict the muscular force response to functional electrical stimulation (FES) and led to optimal control problem, optimizing the force or producing a reference force. The stimulations are Dirac pulses and the control parameters are the pulse amplitude and times of application, the number of pulses is physically limited and the model led to a sampled data control problem. The aim of this article is to present and compare two methods, based on their respective numerical simulations. The first method is a semi-direct optimization scheme where besides the digital control 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 obtain numerical result using a shooting algorithm.
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Toufik Bakir, Bernard Bonnard, Loïc Bourdin, Jérémy Rouot. Indirect and Semi-direct Methods For Optimal Muscular Force Response to Functional Electrical Stimulation. 2019. ⟨hal-02053566⟩

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