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Evolutionary optimisation of Hénon map control: a black box approach

Author

Listed:
  • Roman Senkerik
  • Ivan Zelinka
  • Donald Davendra
  • Zuzana Oplatkova

Abstract

This paper deals with the usage of heuristics for the optimisation of the control of chaotic system. The main aim of this paper is to show a new approach of solving this problem and constructing new cost functions (CFs) operating in 'black box mode' without a previous exact mathematical analysis of the system, thus without knowledge of the stabilising target state. Three proposals of 'black box' mode CFs were tested in this paper. As a model of deterministic chaotic system, the two-dimensional Hénon map was used. The optimisations were realised in several ways, each one for another desired state of system. Evolutionary algorithms (EAs) self-organising migrating algorithm and differential evolution were used. For each version, repeated simulations were conducted to outline the effectiveness and robustness of the used method and CF.

Suggested Citation

  • Roman Senkerik & Ivan Zelinka & Donald Davendra & Zuzana Oplatkova, 2012. "Evolutionary optimisation of Hénon map control: a black box approach," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 13(2), pages 129-146.
    • Handle: RePEc:ids:ijores:v:13:y:2012:i:2:p:129-146
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