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Controlling Chaotic Systems Via Time-Delayed Control

  • R. FaridEmail author
  • A. Ibrahim
  • B. Abou-Zalam
Chapter
  • 953 Downloads
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 307)

Abstract

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua’s circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

Keywords

Chaotic systems Proportional plus integral time-delayed controller Taylor approximation 

References

  1. 1.
    K. Pyragas, Physics Letters A (1992), Continuous control of chaos by self-controlling feedback, 170, 421–428.Google Scholar
  2. 2.
    Maoyin Chen, D. Zhou, Y. Shang, A simple time-delayed method to control chaotic systems (2004), Chaos Solitons Fractals 22, 1117–1125.Google Scholar
  3. 3.
    Maoyin Chen, Y. Shang, D. Zhou, Repetitive learning control of continuous chaotic systems (2004b), Chaos Solitons Fractals, 22, 161–169.Google Scholar
  4. 4.
    Maoyin Chen, D. Zhou, Y. Shang, Integrity control of chaotic systems (2006), Physics Letters A, 350, 214–220.Google Scholar
  5. 5.
    Gunyaz Ablay, Nonlinear Analysis: Hybrid systems (2009), sliding mode control of uncertain unified chaotic systems, 3, 513–535.Google Scholar
  6. 6.
    Congxu Zhu, Nonlinear Analysis (2009), feedback control methods for stabilizing unstable equilibrium points in a new chaotic system, 71, 2441–2446.Google Scholar
  7. 7.
    Congxu Zhu, Z. Chen, Physics Letters A (2008), Feedback control strategies for the Liu chaotic system, 372, 4033–4036.Google Scholar
  8. 8.
    Chaohai Tao, C. Yang, Y. Luo, H. Xiong, F. Hu (2005). Speed feedback control of chaotic system. Chaos Solitons Fractals, 23, 259–263.CrossRefzbMATHGoogle Scholar
  9. 9.
    X. Liao, P. Yu, Chaos control for the family of Rossler systems using feedback controllers Chaos Solitons Fractals 29 (2006) 91–107.Google Scholar
  10. 10.
    X. Wang, L. Tian, S. Jiang, L. Yu, Feedback Control and Synchronization of Chaos for the Coupled Dynamos Dynamical System, Journal of Information and Computing Science, 1 (2006) 2, pp 93–100 ISSN 1746-7659, England, UK.Google Scholar
  11. 11.
    L. Fronzoni, M. Giocondo, CONTROLLING CHAOS WITH PARAMETRIC PERTURBATIONS, International Journal of Bifurcation and Chaos, Vol.8, No.8 (1998) 1693–1698.Google Scholar
  12. 12.
    Lu Jun-an, H. Baoxing, Wu Xiaoqun, Control of a unified chaotic system with delayed continuous periodic switch, Chaos Solitons Fractals 22 (2004) 229–236Google Scholar
  13. 13.
    Xiao F. Wang and G. Chen, Generating topologically conjugate chaotic systems via feedback control (2003), IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL.50, NO. 6, 812–817.Google Scholar
  14. 14.
    Kit-Sang Tang, Kim F. Man, G. Zhong, and G. Chen, Making a continuous-time minimum-phase system chaotic by using time-delay feedback (2001), IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL.48, NO.5,641–645.Google Scholar
  15. 15.
    G. JIANG and W. K. S. TANG, A global synchronization criterion for coupled chaotic systems via unidirectional linear error feedback approach, International Journal of Bifurcation and Chaos, Vol.12, No.10 (2002) 2239–2253.Google Scholar
  16. 16.
    G. JIANG, W. X. Zheng and G. Chen, Global chaos synchronization with channel time-delay, Chaos Solitons Fractals 20 (2004) 267–275.Google Scholar
  17. 17.
    J. M. Peña, Characterizations and stable tests for the Routh conditions and for total positivity Linear Algebra and its Applications 393 (2004) 319–332.Google Scholar
  18. 18.
    R. FARID, A. IBRAHIM, B. ABO-ZALAM, Synchronization of chaotic systems based on observer design under noisy environment, Proceedings of the 10th WSEAS International Conference on Automation & InformationGoogle Scholar
  19. 19.
    R. FARID, A. IBRAHIM, B. ABO-ZALAM, Chaos Synchronization based on PI Fuzzy Observer, Proceedings of the 10th WSEAS International Conference on Fuzzy systemsGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of industrial electronics and control engineering, Faculty of electronic engineeringMenofia UniversityMenufEgypt

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