TY - GEN
T1 - Optimal asymptotic entrainment of phase-reduced oscillators
AU - Zlotnik, Anatoly
AU - Li, Jr Shin
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84863842306&partnerID=8YFLogxK
U2 - 10.1115/DSCC2011-5923
DO - 10.1115/DSCC2011-5923
M3 - Conference contribution
AN - SCOPUS:84863842306
SN - 9780791854754
T3 - ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, DSCC 2011
SP - 479
EP - 484
BT - ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, DSCC 2011
T2 - ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, DSCC 2011
Y2 - 31 October 2011 through 2 November 2011
ER -