Sliding mode control of the Hodgkin-Huxley mathematical model
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.
Keywords
Cite
@article{arxiv.1901.04789,
title = {Sliding mode control of the Hodgkin-Huxley mathematical model},
author = {Cecilia Cavaterra and Denis Enachescu and Gabriela Marinoschi},
journal= {arXiv preprint arXiv:1901.04789},
year = {2020}
}
Comments
18 pages, 18 figures