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Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution

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Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))

Abstract

The paper deals with stabilization of simple deterministic discrete chaotic system. By means of proper utilization of meta-heuristic optimization tool, the HC12 algorithm stands alone and together with a symbolic regression tool, which is Grammatical Evolution (GE), and can synthesise a new control law. Given softcomputing tools appear as powerful optimization tool for an optimal control parameters tuning and general control law design too. The well known one dimensional discrete Logistic equation was used as a model of deterministic chaotic system. Satisfactory results obtained by both heuristics and propose objective function are also compared with previous research of other authors.

The chaotic system stabilization is based on time-delay auto-synchronization (TDAS, ETDAS) and proper combination with own synthesized control law. This synthesized chaotic controller is based on one or two compensator. The primary compensator generates the perturbation sequence using TDAS/ETDAS method, second one is own design using method of GE. The original design of the objective function takes inspiration from standard control theory. All tests are performed using Matlab/Simulink environment.

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Authors and Affiliations

  1. Brno University of Technology, Technicka 2, 61669, Brno, Czech Republic

    Radomil Matousek & Petr Minar

Authors
  1. Radomil Matousek
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  2. Petr Minar
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Correspondence to Radomil Matousek .

Editor information

Editors and Affiliations

  1. Faculty of Electrical Eng. & Comp. Sci, Department of Computer Science, VÅ B-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, China, People's Republic

    Guanrong Chen

  3. , Institute of Physical, University of Tuebingen, Auf der Morgenstelle 8, Tuebingen, 72076, Germany

    Otto E. Rössler

  4. Faculty of Electrical Eng. & Comp. Sci., Department of Computer Science, VÅ B-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Vaclav Snasel

  5. (MIR Labs), Scientific Network for Innovation, Machine Intelligence Research Labs, Auburn, 98071, Washington, USA

    Ajith Abraham

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Matousek, R., Minar, P. (2013). Stabilization of Chaotic Logistic Equation Using HC12 and Grammatical Evolution. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00542-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-00542-3_14

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00541-6

  • Online ISBN: 978-3-319-00542-3

  • eBook Packages: EngineeringEngineering (R0)

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