The Optimal Control of an Excitable Neural Fibre

  • J. E. Rubio
  • A. V. Holden
Part of the NATO ASI Series book series (NSSB, volume 244)


We consider the optimal control of a neural fibre, described by a nonlinear diffusion equation with a polynomial nonlinearity. An iterative scheme is established to compute a minimum-energy control, in which at each step of the iteration a linear problem is solved by means of measure-theoretical methods and linear programming. The method converges for moderate values of the nonlinear terms. Some numerical results are given.


Linear Problem Linear Programming Problem Radon Measure Nonlinear Diffusion Equation Suboptimal Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Casten, R. , Cohen, H. & Langerstrom, P. (1975). Perturbation analysis of an approximation to Hodgkin-Huxley theory. Quart. Appl. Math. 32, 365–378.zbMATHGoogle Scholar
  2. [2]
    Fitzhugh, R. (1969). Mathematical models of excitation and propagation in nerve. In Biological Engineering, Schwan, P. (ed.). McGraw-Hill: New York.Google Scholar
  3. [3]
    Ghouila-Houri, A. (1967). Sur la generalization de la notion de commande d’un système guidable. Revue Française d’Automatique, Informatique, et Recherche Operationelle 4, 7–32.MathSciNetGoogle Scholar
  4. [4]
    Rubio, J.E. (1986). Control and Optimization. Manchester University Press.zbMATHGoogle Scholar
  5. [5]
    Wilson, D.A. & Rubio, J.E. (1977). Existence of optimal controls for the diffusion equation. Journal of Optimization Theory and its Applications 22, 91–100.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    Zykov, V.S. (1988). Simulation of Wave Processes in Excitable Media. Manchester University Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • J. E. Rubio
    • 1
  • A. V. Holden
    • 1
  1. 1.Departments of Mathematics and PhysiologyUniversity of LeedsLeedsUK

Personalised recommendations