Login | Register

A new approach to optimal control of conductance-based spiking neurons

Title:

A new approach to optimal control of conductance-based spiking neurons

Lou, Xuyang and Swamy, M. N. S. (2017) A new approach to optimal control of conductance-based spiking neurons. Neural Networks . ISSN 08936080 (In Press)

[thumbnail of Swamy-NeuralNetworks-2017.pdf]
Preview
Text (application/pdf)
Swamy-NeuralNetworks-2017.pdf - Accepted Version
Available under License Spectrum Terms of Access.
491kB

Official URL: http://dx.doi.org/10.1016/j.neunet.2017.08.011

Abstract

This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on the Pontryagin’s maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Refereed:No
Authors:Lou, Xuyang and Swamy, M. N. S.
Journal or Publication:Neural Networks
Date:11 September 2017
Funders:
  • National Natural Science Foundation of China (61473136)
  • Fundamental Research Funds for the Central Universities (JUSRP51322B)
  • 111 Project ( B12018)
Digital Object Identifier (DOI):10.1016/j.neunet.2017.08.011
Keywords:Spiking neurons; Optimal control; Homotopy perturbation method
ID Code:983026
Deposited By: Danielle Dennie
Deposited On:13 Sep 2017 20:03
Last Modified:01 Sep 2018 00:01

References:

J. Biazar, H. Ghazvini Convergence of the homotopy perturbation method for partial differential equations Nonlinear Analysis. Real World Applications, 10 (2009), pp. 2633–2640

W.A. Cebuhar, V. Constanza Approximation procedures for the optimal control of bilinear and nonlinear systems Journal of Optimization Theory and Applications, 43 (4) (1984), pp. 615–627

P. Danzl, J. Hespanha, J. Moehlis Event-based minimum-time control of oscillatory neuron models: phase randomization, maximal spike rate increase, and desynchronization Biological Cybernetics, 101 (2009), pp. 387–399

I. Dasanayake, J.S. Li Optimal design of minimum-power stimuli for phase models of neuron oscillators Physical Review E, 83 (2011) Article No. 061916

Dasanayake, I., & Li, J. S. (2013). Optimal control of neurons using the homotopy perturbation method. In The 52nd IEEE conference on decision and control, December 10–13, Florence, Italy (pp. 3385–3390).

I. Dasanayake, J.S. Li Charge-balanced minimum-power controls for spiking neuron oscillators Systems & Control Letters, 75 (2015), pp. 124–130

M. Ellinger, M.E. Koelling, D.A. Miller, F.L. Severance, J. Stahl Exploring optimal current stimuli that provide membrane voltage tracking in a neuron model Biological Cybernetics, 104 (2011), pp. 185–195

X.J. Feng, E. Shea-Brown, B. Greenwald, R. Kosut, H. Rabitz Optimal deep brain stimulation of the subthalamic nucleus-a computational study Journal of Computational Neuroscience, 23 (3) (2007), pp. 265–282

R. FitzHugh Impulses and physiological states in theoretical models of nerve membrane Biophysical Journal, 1 (6) (1961), pp. 445–466

A. Ghorbani Beyond Adomian polynomials: He polynomials Chaos, Solitons & Fractals, 39 (3) (2009), pp. 1486–1492

J.H. He An approximate solution technique depending upon an artificial parameter Communications in Nonlinear Science, 3 (2) (1998), pp. 92–97

J.H. He Homotopy perturbation technique Computer Methods in Applied Mechanics and Engineering, 178 (1999), pp. 257–262

J.H. He Homotopy perturbation method: a new nonlinear analytical technique Applied Mathematics and Computation, 135 (1) (2003), pp. 73–79

J. Hindmarsh, P. Cornelius The development of the Hindmarsh-Rose model for bursting S. Coombes, P.C. Bressloff (Eds.), Bursting: the genesis of rhythm in the nervous system, World Scientific Publishing, Singapore (2005), pp. 3–18

G.T. Huntington, A.V. Rao Optimal reconfiguration of spacecraft formations using the gauss pseudospectral method Journal of Guidance, Control, and Dynamics, 31 (3) (2008), pp. 689–698

I.E. Izhikevich Dynamical systems in neuroscience, The MIT Press, Cambridge, Massachusetts (2007)

A. Jajarmi, N. Pariz, A. Vahidian Kamyad, S. Effati A highly computational efficient method to solve nonlinear optimal control problems Scientia Iranica D, 19 (3) (2012), pp. 759–766

Keener, J., & Sneyd, J. (2000). Mathematical physiology, Springer, New York.

J. Moehlis, E. Shea-Brown, H. Rabitz Optimal inputs for phase models of spiking neurons Journal of Computational and Nonlinear Dynamics, 1 (4) (2006), pp. 358–367

A. Nabi, M. Mirzadeh, F. Gibou, J. Moehlis Minimum energy desynchronizing control for coupled neurons Journal of Computational Neuroscience, 34 (2013), pp. 259–271

A Nabi, J. Moehlis Single input optimal control for globally coupled neuron networks Journal of Neural Engineering, 8 (2011) Article No. 065008

A. Nabi, T. Stigen, J. Moehlis, T. Netoff Minimum energy control for in vitro neurons Journal of Neural Engineering, 10 (2013) Article No. 036005

J. Nagumo, S. Arimoto, S. Yoshizawa An active pulse transmission line simulating nerve axon Proceedings of the IRE, 50 (10) (1962), pp. 2061–2070

J.E. Niven, S.B. Laughlin Energy limitation as a selective pressure on the evolution of sensory systems Journal of Fish Biology, 211 (Pt11) (2008), pp. 1792–1804

A.V. Rao, D.A. Benson, C.L. Darby, et al. GPOPS: a Matlab software for solving multiple-phase optimal control problems using the gauss pseudospectral method ACM Transactions on Mathematical Software, 37 (2) (2010), pp. 1–39

G. Reddy, C. Murthy Coherence resonance in the FitzHugh-Nagumo system, University of California, San Diego (2013) Physics 210B: Nonequilibrium Statistical Physics, Student Project

B. Sengupta, M. Stemmler, S.B. Laughlin, J.E. Niven Action potential energy efficiency varies among neuron types in vertebrates and invertebrates PLoS Computational Biology, 6 (7) (2010), p. e1000840

Shampine, L. F., Kierzenka, J., & Reichelt, M. W. (2010). Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c. weblink, October 8.

T. Stigen, P. Danzl, J. Moehlis, T. Netoff Controlling spike timing and synchrony in oscillatory neurons Journal of Neurophysiology, 105 (5) (2011), pp. 2074–2082

J. Sun, W.L. Yang Optimal control of the Fitzhugh-Hagumo neurons systems in general form Pacific Journal of Optimization, 12 (4) (2016), pp. 757–774

G.T. Tang Suboptimal control for nonlinear systems: a successive approximation approach Systems & Control Letters, 54 (5) (2005), pp. 429–434

Y. Tsubo, T. Kaneko, S. Shinomoto Predicting spike timings of current-injected neurons Neural Networks, 2 (2004), pp. 165–173

D. Wilson, A.B. Holt, T.I. Netoff, J. Moehlis Optimal entrainment of heterogeneous noisy neurons Frontiers in Neuroscience, 9 (2015), pp. 1–10 article 192

G.S. Yi, J. Wang, H.Y. Li, X.L. Wei, B. Deng Minimum energy control for a two-compartment neuron to extracellular electric fields Communications in Nonlinear Science and Numerical Simulation, 40 (2016), pp. 138–150

Q. Yu, H.J. Tang, K.C. Tan, H.Z. Li Rapid feedforward computation by temporal encoding and learning with spiking neurons IEEE Transactions on Neural Networks and Learning Systems, 24 (10) (2013), pp. 1539–1552
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top