Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle

Yuan Jiang; Jiyang Dai

Kybernetika (2011)

  • Volume: 47, Issue: 4, page 612-629
  • ISSN: 0023-5954

Abstract

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This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then we apply the obtained output regulation results to the control problem for modified FitzHugh-Nagumo neuron model. Finally, an output feedback control law is designed for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation generated from a Van der Pol circuit.

How to cite

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Jiang, Yuan, and Dai, Jiyang. "Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle." Kybernetika 47.4 (2011): 612-629. <http://eudml.org/doc/196901>.

@article{Jiang2011,
abstract = {This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then we apply the obtained output regulation results to the control problem for modified FitzHugh-Nagumo neuron model. Finally, an output feedback control law is designed for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation generated from a Van der Pol circuit.},
author = {Jiang, Yuan, Dai, Jiyang},
journal = {Kybernetika},
keywords = {control theory; Lyapunov methods; internal model principle; modified FitzHugh--Nagumo model; Van der Pol circuit; Van der Pol circuit; control theory; Lyapunov methods; internal model principle; modified Fitzhugh-Nagumo model},
language = {eng},
number = {4},
pages = {612-629},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle},
url = {http://eudml.org/doc/196901},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Jiang, Yuan
AU - Dai, Jiyang
TI - Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 4
SP - 612
EP - 629
AB - This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output regulation problem for the modified FitzHugh-Nagumo neuron model are all satisfied. Then we apply the obtained output regulation results to the control problem for modified FitzHugh-Nagumo neuron model. Finally, an output feedback control law is designed for the modified FitzHugh-Nagumo neuron model to achieve global stability of the closed-loop system in the presence of uncertain parameters and external stimulus. An example is shown that the proposed algorithm can completely reject the external electrical stimulation generated from a Van der Pol circuit.
LA - eng
KW - control theory; Lyapunov methods; internal model principle; modified FitzHugh--Nagumo model; Van der Pol circuit; Van der Pol circuit; control theory; Lyapunov methods; internal model principle; modified Fitzhugh-Nagumo model
UR - http://eudml.org/doc/196901
ER -

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