Observer Design for the Hodgkin-Huxley Neuronal Model

Meric Cetin [1] , Selami Beyhan [2]


Hodgkin-Huxley (HH) neuronal model has been widely accepted neuronal model in neuroscience. The variation of the ionic currents in neuron cell causes the variations in the membrane potential. The level of membrane potential indicates the activation and inactivation dynamics. In this paper, in order to observe the unmeasurable states and parameters of HH neuron accurately, Runge-Kutta discretization based nonlinear observer is designed. In numerical simulations, the membrane potential is measured and the ionic currents are estimated. The numerical results provide accurate estimation results that can be used both in monitoring and control of neuron dynamics.
Nonlinear observer, state estimation, Hodgkin-Huxley neuronal model, discretization based gradient observer, sliding-mode observer, extended Kalman filter
  • [1] Dayan, P.; Abbott, L. (2005). Theoretical Neuroscience: Computational &Mathematical modelling of neural systems. ISBN-10: 0262541858. MIT Press.
  • [2] Hodgkin, A.; Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology 117: (4), 500–544.
  • [3] Neefs, P. J.; Steur, E.; Nijmeijer, (2010). H. Network complexity and synchronous behavior - an experimental approach. International Journal of Neural Systems 20: (03), 233–247.
  • [4] Dahasert, N.; Öztürk, İ.; Kılıç, R. (2012). Experimental realizations of the HR neuron model with programmable hardware and synchronization applications. Nonlinear Dynamics 70: (4), 2343–2358.
  • [5] Li, W.; Cheung, R.; Chan, R.; Song, D.; Berger, T. (2013). Real-time prediction of neuronal population spiking activity using fpga. Biomedical Circuits and Systems, IEEE Transactions on 7: (4), 489–498.
  • [6] Luenberger, D. (1966). Observers for multivariable systems. IEEE Trans. Autom. Control 11: (2), 190–197.
  • [7] Thau, E.E. (1973). Observing the state of nonlinear systems. Int.J. Control 17: 471–479.
  • [8] Birk, J.; Zeitz, M. (1988). Extended-Luenberger observer for non-linear multivariable systems. Int. J. Control 47: (6), 1823–1836.
  • [9] Cox, H. (1964). On the estimation of state variables and parameters for noisy dynamic systems. IEEE Trans. Autom. Control 9: (1), 5–12.
  • [10] Drakunov, S.V. (1983). An adaptive quasioptimal filter with discontinuous parameters. Autom. Remote Control 44: (9), 1167–1175.
  • [11] Slotine, J. J.; Hedrick, J. K.; Misawa, E. A. (1987). On sliding observers for nonlinear systems. Journal of Dynamic Systems, Measurement, and Controlv109: (3), 245-252.
  • [12] Gauthier, J.P.; Hammouri, H.; Othman, S. (1992). A simple observer for nonlinear systems applications to bioreactors. IEEE Trans. Autom. Control 37: (6), 875–880.
  • [13] Tanaka, K.; Wang, H.O. (1997). Fuzzy regulators and fuzzy observers: a linear matrix inequality approach. In: Proceedings of the 36th IEEE Conference on Decision and Control (2) 1315–1320, San Diego, California.
  • [14] Beyhan, S. (2013). Runge–Kutta model-based nonlinear observer for synchronization and control of chaotic systems. ISA Trans. 52: (4), 501–509.
  • [15] Cetin, M.; Beyhan, S.; Iplikci, S. (2016). Soft sensor applications of RK-based nonlinear observers and experimental comparisons. Intelligent Automation & Soft Computing, DOI: 10.1080/10798587.2016.1147763
  • [16] İplikci, S. (2013). Runge–Kutta model-based adaptive predictive control mechanism for non-linear processes. Trans. Inst. Meas. Control 35: (2), 166–180.
  • [17] Butcher, J. C. (1987). The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods. Wiley-Interscience.
  • [18] Spurgeon, S.K. (2008). Sliding mode observers: a survey. Int. J. Syst.Sci.39: (8), 751–764.
  • [19] Hosani, Al.; Utkin, K. (2012). Parameters estimation using sliding mode observer with shift operator. J. Frankl. Inst. 349: (4),1509–1525.
Subjects Engineering
Journal Section Research Article
Authors

Author: Meric Cetin
Institution: PAMUKKALE UNIV
Country: Turkey


Author: Selami Beyhan
Institution: PAMUKKALE UNIV
Country: Turkey


Dates

Publication Date : December 1, 2016

Bibtex @research article { ijamec265327, journal = {International Journal of Applied Mathematics Electronics and Computers}, issn = {}, eissn = {2147-8228}, address = {}, publisher = {Selcuk University}, year = {2016}, volume = {}, pages = {66 - 71}, doi = {10.18100/ijamec.265327}, title = {Observer Design for the Hodgkin-Huxley Neuronal Model}, key = {cite}, author = {Cetin, Meric and Beyhan, Selami} }
APA Cetin, M , Beyhan, S . (2016). Observer Design for the Hodgkin-Huxley Neuronal Model. International Journal of Applied Mathematics Electronics and Computers , (Special Issue-1) , 66-71 . DOI: 10.18100/ijamec.265327
MLA Cetin, M , Beyhan, S . "Observer Design for the Hodgkin-Huxley Neuronal Model". International Journal of Applied Mathematics Electronics and Computers (2016 ): 66-71 <https://dergipark.org.tr/en/pub/ijamec/issue/25619/265327>
Chicago Cetin, M , Beyhan, S . "Observer Design for the Hodgkin-Huxley Neuronal Model". International Journal of Applied Mathematics Electronics and Computers (2016 ): 66-71
RIS TY - JOUR T1 - Observer Design for the Hodgkin-Huxley Neuronal Model AU - Meric Cetin , Selami Beyhan Y1 - 2016 PY - 2016 N1 - doi: 10.18100/ijamec.265327 DO - 10.18100/ijamec.265327 T2 - International Journal of Applied Mathematics Electronics and Computers JF - Journal JO - JOR SP - 66 EP - 71 VL - IS - Special Issue-1 SN - -2147-8228 M3 - doi: 10.18100/ijamec.265327 UR - https://doi.org/10.18100/ijamec.265327 Y2 - 2016 ER -
EndNote %0 International Journal of Applied Mathematics Electronics and Computers Observer Design for the Hodgkin-Huxley Neuronal Model %A Meric Cetin , Selami Beyhan %T Observer Design for the Hodgkin-Huxley Neuronal Model %D 2016 %J International Journal of Applied Mathematics Electronics and Computers %P -2147-8228 %V %N Special Issue-1 %R doi: 10.18100/ijamec.265327 %U 10.18100/ijamec.265327
ISNAD Cetin, Meric , Beyhan, Selami . "Observer Design for the Hodgkin-Huxley Neuronal Model". International Journal of Applied Mathematics Electronics and Computers / Special Issue-1 (December 2016): 66-71 . https://doi.org/10.18100/ijamec.265327
AMA Cetin M , Beyhan S . Observer Design for the Hodgkin-Huxley Neuronal Model. International Journal of Applied Mathematics Electronics and Computers. 2016; (Special Issue-1): 66-71.
Vancouver Cetin M , Beyhan S . Observer Design for the Hodgkin-Huxley Neuronal Model. International Journal of Applied Mathematics Electronics and Computers. 2016; (Special Issue-1): 71-66.