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Parametric convergence and control of chaotic system using adaptive feedback linearization

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  • Sharma, B.B.
  • Kar, I.N.

Abstract

Adaptive feedback linearization control technique for chaos suppression in a chaotic system is proposed. The dynamics of the system is altered so that the closed loop model matches with a specified linear reference model. The controller parameters are assumed to be unknown and are evolved using an adaptation law that aims to drive these parameters towards their ideal values so as to achieve perfect matching between the reference and the system model. A common external forcing signal to both chaotic Genesio system and reference system is considered and adaptation laws are derived considering Lyapunov function based stability. Simulation results show that the chaotic behavior is suppressed effectively with proposed controller. Analysis of linear and nonlinear parametric convergence is also shown through simulation, both with and without excitation using suitable forcing function.

Suggested Citation

  • Sharma, B.B. & Kar, I.N., 2009. "Parametric convergence and control of chaotic system using adaptive feedback linearization," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1475-1483.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1475-1483
    DOI: 10.1016/j.chaos.2007.09.060
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    References listed on IDEAS

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    1. Chang, Wei-Der & Yan, Jun-Juh, 2005. "Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 167-175.
    2. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    3. Yassen, M.T., 2006. "Chaos control of chaotic dynamical systems using backstepping design," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 537-548.
    4. Jayaram, A. & Tadi, M., 2006. "Synchronization of chaotic systems based on SDRE method," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 707-715.
    5. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
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    Cited by:

    1. Handa, Himesh & Sharma, B.B., 2016. "Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 50-63.
    2. Sharma, B.B. & Kar, I.N., 2011. "Stabilization and tracking controller for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 902-913.
    3. Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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