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arXiv · 1901.04789

Sliding mode control of the Hodgkin-Huxley mathematical model

Cecilia Cavaterra·Denis Enachescu·Gabriela Marinoschi
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Abstract

In this paper we deal with a feedback control design for the action potential of a neuronal membrane in relation with the non-linear dynamics of the Hodgkin-Huxley mathematical model. More exactly, by using an external current as a control expressed by a relay graph in the equation of the potential, we aim at forcing it to reach a certain manifold in finite time and to slide on it after that. From the mathematical point of view we solve a system involving a parabolic differential inclusion and three nonlinear differential equations via an approximating technique and a fixed point result. The existence of the sliding mode and the determination of the time at which the potential reaches the prescribed manifold is proved by a maximum principle argument. Numerical simulations are presented.

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Cecilia Cavaterra, Denis Enachescu, Gabriela Marinoschi. 2019-01-15. Sliding mode control of the Hodgkin-Huxley mathematical model. https://doi.org/10.3934/eect.2019043

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