Adapting predictive feedback chaos control for optimal convergence speed

Christian Bick*, Marc Timme, Christoph Kolodziejski

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)1310-1324
Number of pages15
JournalSIAM Journal on Applied Dynamical Systems
Issue number4
Publication statusPublished - 26 Dec 2012
Externally publishedYes


  • Adaptation
  • Asymptotic convergence speed
  • Chaos control
  • Predictive feedback control


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