A recent force-fatigue parameterized mathematical model, based on the seminal contributions of V. Hill to describe muscular activity, allows to predict the muscular force response to external electrical stimulation (FES) and it opens the road to optimize the FES-input to maximize the force response to a pulse train, to track a reference force while minimizing the fatigue for a sequence of pulse trains or to follow a reference joint angle trajectory to produce motion in the non-isometric case. In this article, we introduce the geometric frame to analyze the dynamics and we present Pontryagin types necessary optimality conditions adapted to digital controls, used in the experiments, vs permanent control and which fits in the optimal sampled-data control frame. This leads to Hamiltonian differential variational inequalities, which can be numerically implemented vs direct optimization schemes.

中文翻译：

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使用非等距力-疲劳模型来控制肌肉对功能性电刺激反应的几何优化技术

基于V.Hill的主要贡献来描述肌肉活动的最新力量疲劳参数化数学模型，可以预测肌肉力量对外部电刺激（FES）的反应，这为优化FES输入以最大化最大化开辟了道路。力响应脉冲序列，以跟踪参考力，同时最大程度减少一系列脉冲序列的疲劳，或者遵循参考关节角度轨迹以在非等距情况下产生运动。在本文中，我们介绍了用于分析动力学的几何框架，并介绍了Pontryagin类型的必要最优条件，这些条件适用于实验中使用的数字控件和永久控件，并且适合于最佳采样数据控件框架。这导致了哈密顿微分变分不等式，