Identification of biological neurons using adaptive observers

This paper is to investigate the use of adaptive observers for the modeling of biological neurons and networks. Assuming that a neuron can be modeled as a continuous-time nonlinear system, it is possible to determine its unknown parameters using adaptive observer, based on the concept of adaptive synchronization. The same technique can be extended for the identification of an entire biological neural network. Some conventional observer designs are studied in this paper and satisfactory results are obtained, yet with some restrictions. To further extend the applicability of adaptive observers for the modeling process, a new design is suggested. It is based on a combination of linear feedback control approach and the dynamical minimization algorithm. The effectiveness of the designed adaptive observer is confirmed with simulations.

[1]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[2]  Wojciech Cholewa,et al.  Fault Diagnosis , 2004, Springer Berlin Heidelberg.

[3]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[4]  R. Marino,et al.  Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems , 1995, IEEE Trans. Autom. Control..

[5]  Carroll,et al.  Driving systems with chaotic signals. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[6]  Ljupco Kocarev,et al.  An Adaptive Observer Design for Auto-Synchronization of Lorenz System , 2008, Int. J. Bifurc. Chaos.

[7]  Xiao-Jing Wang,et al.  Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle , 1993 .

[8]  Qinghua Zhang.  A new residual generation and evaluation method for detection and isolation of faults in non‐linear systems , 2000 .

[9]  R. Marino.  Adaptive observers for single output nonlinear systems , 1990 .

[10]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  Bin Jiang,et al.  Fault diagnosis based on adaptive observer for a class of non-linear systems with unknown parameters , 2004 .

[12]  Qinghua Zhang,et al.  Revisiting different adaptive observers through a unified formulation , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[13]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[14]  Changsong Zhou,et al.  Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations , 2000 .

[15]  B. Delyon,et al.  A new approach to adaptive observer design for MIMO systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[16]  R. Marino,et al.  Global adaptive observers for nonlinear systems via filtered transformations , 1992 .

[17]  Murat Arcak,et al.  An adaptive observer design for fuel cell hydrogen estimation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[18]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[19]  M. Gevers,et al.  Stable adaptive observers for nonlinear time-varying systems , 1987 .

[20]  India,et al.  Use of synchronization and adaptive control in parameter estimation from a time series , 1998, chao-dyn/9804005.

[21]  Amritkar,et al.  Dynamic algorithm for parameter estimation and its applications , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  P. Frank,et al.  An Adaptive Observer-Based Fault Detection Scheme for Nonlinear Dynamic Systems , 1993 .