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Cognitive Neurodynamics
Erschienen in: Cognitive Neurodynamics 1/2019

15.10.2018 | Research Article

Nonlinear optimal control for the synchronization of biological neurons under time-delays

verfasst von: G. Rigatos, P. Wira, A. Melkikh

Erschienen in: Cognitive Neurodynamics | Ausgabe 1/2019

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Abstract

The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh–Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller’s feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.
Vorheriger Artikel Energy expenditure computation of a single bursting neuron
Nächster Artikel The impact of spike-frequency adaptation on balanced network dynamics

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Metadaten
Titel
Nonlinear optimal control for the synchronization of biological neurons under time-delays
verfasst von
G. Rigatos
P. Wira
A. Melkikh
Publikationsdatum
15.10.2018
Verlag
Springer Netherlands
Erschienen in
Cognitive Neurodynamics / Ausgabe 1/2019
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-018-9510-4

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