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Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed

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Bick,  Christian
Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Timme,  Marc
Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Kolodziejski,  Christoph
Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Bick, C., Timme, M., & Kolodziejski, C. (2012). Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed. SIAM Journal on Applied Dynamical Systems, 11(4), 1310-1324. doi:10.1137/120861618.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-1071-B
Abstract
Stabilizing unstable periodic orbits in a chaotic invariant set not only reveals information about its structure but also leads to various interesting applications. For the successful application of a chaos control scheme, convergence speed is of crucial importance. Here we present a predictive feedback chaos control method that adapts a control parameter online to yield optimal asymptotic convergence speed. We study the adaptive control map both analytically and numerically and prove that it converges at least linearly to a value determined by the spectral radius of the control map at the periodic orbit to be stabilized. The method is easy to implement algorithmically and may find applications for adaptive online control of biological and engineering systems.