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Indirect adaptive control of discrete chaotic systems

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  • Salarieh, Hassan
  • Shahrokhi, Mohammad

Abstract

In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations.

Suggested Citation

  • Salarieh, Hassan & Shahrokhi, Mohammad, 2007. "Indirect adaptive control of discrete chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1188-1201.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1188-1201
    DOI: 10.1016/j.chaos.2006.03.115
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    References listed on IDEAS

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    1. Alasty, Aria & Salarieh, Hassan, 2005. "Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 379-392.
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    Cited by:

    1. Salarieh, Hassan & Alasty, Aria, 2008. "Delayed feedback control via minimum entropy strategy in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 851-860.
    2. Rani, Mamta & Agarwal, Rashi, 2009. "A new experimental approach to study the stability of logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2062-2066.
    3. dos Santos Coelho, Leandro & Coelho, Antonio Augusto Rodrigues, 2009. "Model-free adaptive control optimization using a chaotic particle swarm approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2001-2009.
    4. Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing unstable fixed points of chaotic maps via minimum entropy control," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 763-769.
    5. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    6. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in uncertain dynamical systems using nonlinear delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 67-71.
    7. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
    8. Rani, Mamta & Agarwal, Rashi, 2009. "Generation of fractals from complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 447-452.
    9. Coelho, Leandro dos Santos & Araujo, Ernesto, 2009. "Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2762-2772.
    10. Layeghi, Hamed & Arjmand, Mehdi Tabe & Salarieh, Hassan & Alasty, Aria, 2008. "Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1125-1135.
    11. Zelinka, Ivan & Senkerik, Roman & Navratil, Eduard, 2009. "Investigation on evolutionary optimization of chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 111-129.
    12. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive control of chaotic systems with stochastic time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 168-177.

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