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Stabilizing unstable fixed points of chaotic maps via minimum entropy control

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  • Salarieh, Hassan
  • Alasty, Aria

Abstract

In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:763-769
    DOI: 10.1016/j.chaos.2006.09.062
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    References listed on IDEAS

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    1. Salarieh, Hassan & Shahrokhi, Mohammad, 2007. "Indirect adaptive control of discrete chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1188-1201.
    2. Alasty, Aria & Salarieh, Hassan, 2007. "Nonlinear feedback control of chaotic pendulum in presence of saturation effect," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 292-304.
    3. Mohammad Shahrokhi, 2011. "Adaptive Control of Chaos," Chapters, in: Esteban Tlelo-Cuautle (ed.), Chaotic Systems, IntechOpen.
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    Cited by:

    1. Zhang, Yinping & Sun, Jitao, 2009. "Impulsive robust fault-tolerant feedback control for chaotic Lur’e systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1440-1446.
    2. Vázquez-Medina, R. & Díaz-Méndez, A. & del Río-Correa, J.L. & López-Hernández, J., 2009. "Design of chaotic analog noise generators with logistic map and MOS QT circuits," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1779-1793.
    3. 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.
    4. Kevin W. Capehart, 2015. "Hyman Minsky’s interpretation of Donald Trump," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 38(3), pages 477-492, October.

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