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Optimal Asymptotic Entrainment of Phase-Reduced Oscillators

[+] Author Affiliations
Anatoly Zlotnik, Jr-Shin Li

Washington University, Saint Louis, MO

Paper No. DSCC2011-5923, pp. 479-484; 6 pages
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control
  • ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1
  • Arlington, Virginia, USA, October 31–November 2, 2011
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5475-4
  • Copyright © 2011 by ASME


We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space representation of the oscillator is reduced to a linearized phase model, and the optimal periodic control is computed from the phase response curve using formal averaging and the calculus of variations. Computational methods are used to calculate the periodic orbit and the phase response curve, and a numerical method for approximating the optimal controls is introduced. Our method is applied to asymptotically control the period of spiking neural oscillators modeled using the Hodgkin-Huxley equations. This example illustrates the optimality of entrainment controls derived using phase models when applied to the original state space system.

Copyright © 2011 by ASME



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