A Note about Robust Stabilization of Chaotic Hénon System Using Grammatical Evolution

  • Radomil Matousek
  • Ladislav Dobrovsky
  • Petr Minar
  • Katerina Mouralova
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 289)


The paper deals with robust stabilization of a well-known deterministic discrete chaotic system denoted as Hénon map. By means of proper utilization of metaheuristic optimization tool, the Grammatical Evolution (GE) can synthesise a new robust control law. As a model of deterministic chaotic system the two-dimensional Hénon map with original definition was used. The Hénon map is an iterated discrete-time system which exhibits chaotic behaviour in two-dimension. Stabilization for the period-2 orbits of the two-dimensional Hénon map is presented. The chaotic system stabilization is based on a time-delay auto-synchronization with its own synthesized control law. This synthesized chaotic controller utilizes own design of advanced GE algorithm with two-level optimization procedures and a proper objective function. The original objective function design considers a low sensitivity dependence on initial conditions and also proper time for stabilisation of the control process. All computing experiments are performed using Matlab/Simulink environment where the double precision floating point arithmetic was used.


Hénon map Chaos Control Robust stabilization Metaheuristic optimization Grammatical evolution 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Radomil Matousek
    • 1
  • Ladislav Dobrovsky
    • 1
  • Petr Minar
    • 1
  • Katerina Mouralova
    • 1
  1. 1.Department of Applied Computer ScienceBrno University of TechnologyBrnoCzech Republic

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