Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Time-delayed feedback and neural networks
DY 7.4: Talk
Monday, February 25, 2008, 17:15–17:30, A 053
Observing global properties of time-delayed feedback control with an unstable controller — •Hiroyuki Shirahama1,2, Klaus Höhne1, Hartmut Benner1, and Wolfram Just3 — 1Institut für Festkörperphysik, TU Darmstadt,, 64289 Darmstadt, Germany — 2Faculty of Education, Ehime University, Matsuyama 790-8577, Japan — 3Queen Mary/University of London, School of Mathematical Sciences, London E1 4NS, UK
Time-delayed feedback control is a simple, robust and efficient tool to stabilize unstable periodic orbits embedded in strange attractors of chaotic systems. Early analytical investigations indicated that unstable orbits with an odd number of real unstable modes cannot be stabilized by this method [1]. To overcome this limitation the counterintuitive idea of an unstable control loop has been proposed [2]. By including an additional unstable mode into the control loop one artificially enlarges the set of real multipliers greater than unity to an even number. We demonstrate the feasibility of an unstable control loop to stabilize such torsion-free orbits in an electronic circuit experiment. Analytical normal form calculations and numerical simulations reveal a severe dependence of the control performance on the coupling scheme of the control force. These predictions are confirmed by the experiment and emphasize the importance of the coupling scheme for the global control performance [3].
[1] H. Nagajima, Phys. Lett. A 232, 207 (1997)
[2] K. Pyragas, Phys. Rev. Lett. 86, 2265 (2001)
[3] K. Höhne et al., Phys. Rev. Lett. 98, 214102 (2007)