Adaptive tuning of feedback gain in time-delayed feedback control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2011-12, Vol.21 (4), p.043111-043111-6
Main Authors: Lehnert, J., Hövel, P., Flunkert, V., Guzenko, P. Yu, Fradkov, A. L., Schöll, E.
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Feedback
Models, Statistical
Nonlinear Dynamics
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Summary:We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.3647320