In this talk, we present the different issues to design of a smart electrostimu- lator for muscle rehabilitation or reinforcement, in order to control the muscular force or to regulate to a force level. First of all he Ding et al model validated by previous human experiments is used to model the force response to a train of electrical stimulations. It is based of the Hill’s muscle model (Medecine No- blel price 1922)] which describes the dynamics relating the ca+concentration to the force response.The main features of this non nonlinear dynamics being the muscle memory to successive stimulations and the saturation of the force called tetany. An important aspect of the project being to model and identify the fatigue during a training session where each training session limited to 30 mins can cause severe fatigue due to external stimulations. The electrostimulator is based on two training programs related to muscular rehabilitation or reinforce- ment. A first “punch program” aims to maximize the force response to a single train of impulsions of around 500 ms. A finite dimensional approximation of the non-fatigue model is constructed to bypass the computational complexity due to the integration of the dynamics. The model and the approximation depends upon the same set formed by 6 parameters of the non-fatigue model. The second program related to (“marathon runner”) endurance is to regulate the muscle to a constant force while minimizing the fatigue. An internal input-output model is constructed to achieve this task and the control sequence is computed during the session in real time using a MPC method.The second aim of our talk is to analyze the estimation problem of the parameters. It is based on the prelimi- nary experiments. Among the total set of parameters four are not depending on the individuals and they can be scanned at the beginning of the session. Four additional parameters are associated to the model where the fatigue is analyzed online. An software sensor is described using mainly the piezzo-electric force sensor to obtain parameters estimates during the “rest periods” in the session. It is based on recent results in geometric estimation obtained in the 2000’s for nonlinear systems where the bad (non persistent) inputs have to be identified and the construction of the estimator uses normal “linearizing” coordinates. The specificity of the input-output model allows to make the explicit computations.

https://indico.math.cnrs.fr/event/11709/