Journal of Applied Mathematics

Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances

Qing Wang, Yongguang Yu, and Hu Wang

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Abstract

The robust synchronization of hyperchaotic systems with uncertainties and external disturbances is investigated. Based on the Lyapunov stability theory, the appropriate adaptive controllers and parameter update laws are designed to achieve the synchronization of uncertain hyperchaotic systems. The robust synchronization of two hyperchaotic Chen systems is taken as an example to verify the feasibility of the presented schemes. The size of the subcontroller gain’s influences on the convergence speed is discussed. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed synchronization schemes.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 523572, 8 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305667

Digital Object Identifier
doi:10.1155/2014/523572

Zentralblatt MATH identifier
07010665

Citation

Wang, Qing; Yu, Yongguang; Wang, Hu. Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances. J. Appl. Math. 2014 (2014), Article ID 523572, 8 pages. doi:10.1155/2014/523572. https://projecteuclid.org/euclid.jam/1425305667


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References

  • L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990.
  • G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives, and Applications, vol. 24 of World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, World Scientific Publishing, River Edge, NJ, USA, 1998.
  • L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Physical Review A, vol. 44, no. 4, pp. 2374–2383, 1991.
  • X. Wang and Y. Wang, “Adaptive generalized synchronization of hyperchaos systems,” International Journal of Modern Physics B, vol. 25, no. 32, pp. 4563–4571, 2011.
  • Y. Yu, H.-X. Li, and J. Yu, “Generalized synchronization of different dimensional chaotic systems based on parameter identification,” Modern Physics Letters B, vol. 23, no. 22, pp. 2593–2606, 2009.
  • P. Liu and S. Liu, “Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances,” Nonlinear Dynamics, vol. 70, no. 1, pp. 585–599, 2012.
  • E. E. Mahmoud, “Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 349, no. 3, pp. 1247–1266, 2012.
  • C.-C. Yang, “Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller,” Nonlinear Dynamics, vol. 63, no. 3, pp. 447–454, 2011.
  • N. Smaoui, A. Karouma, and M. Zribi, “Adaptive synchronization of hyperchaotic chen systems with application to secure communication,” International Journal of Innovative Computing, Information and Control, vol. 9, no. 3, pp. 1127–1144, 2013.
  • G. M. Mahmoud and E. E. Mahmoud, “Modified projective lag synchronization of two nonidentical hyperchaotic complex nonlinear systems,” International Journal of Bifurcation and Chaos, vol. 21, no. 8, pp. 2369–2379, 2011.
  • Y.-A. Zheng, “Adaptive generalized projective synchronization of takagi-sugeno fuzzy drive-response dynamical networks with time delay,” Chinese Physics Letters, vol. 29, no. 2, Article ID 020502, 2012.
  • Z.-Y. Wu and X.-C. Fu, “Adaptive function projective synchronization of discrete chaotic systems with unknown parameters,” Chinese Physics Letters, vol. 27, no. 5, Article ID 050502, 2010.
  • C. Ma and X. Wang, “Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals,” Nonlinear Dynamics, vol. 70, no. 1, pp. 551–558, 2012.
  • M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Physical Review Letters, vol. 78, no. 22, pp. 4193–4196, 1997.
  • E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, “Lag synchronization in time-delayed systems,” Physics Letters A, vol. 292, no. 6, pp. 320–324, 2002.
  • H. Du, Q. Zeng, C. Wang, and M. Ling, “Function projective synchronization in coupled chaotic systems,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 705–712, 2010.
  • H. Du, F. Li, and G. Meng, “Robust function projective synchronization of two different chaotic systems with unknown parameters,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 348, no. 10, pp. 2782–2794, 2011.
  • Y. Yu and H.-X. Li, “Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 388–393, 2011.
  • C.-L. Kuo, “Design of a fuzzy sliding-mode synchronization controller for two different chaos systems,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2090–2095, 2011.
  • N.-S. Pai, H.-T. Yau, and C.-L. Kuo, “Fuzzy logic combining controller design for chaos control of a rod-type plasma torch system,” Expert Systems with Applications, vol. 37, no. 12, pp. 8278–8283, 2010.
  • W. Guo, S. Chen, and H. Zhou, “A simple adaptive-feedback controller for chaos synchronization,” Chaos, Solitons & Fractals, vol. 39, no. 1, pp. 316–321, 2009.
  • J. M. V. Grzybowski, M. Rafikov, and J. M. Balthazar, “Synchronization of the unified chaotic system and application in secure communication,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 6, pp. 2793–2806, 2009.
  • S. M. Lee, D. H. Ji, J. H. Park, and S. C. Won, “${H}_{\infty }$ synchronization of chaotic systems via dynamic feedback approach,” Physics Letters A, vol. 372, no. 29, pp. 4905–4912, 2008.
  • M. Srivastava, S. K. Agrawal, and S. Das, “Adaptive projective synchronization between different chaotic systems with parametric uncertainties and external disturbances,” Pramana–-Journal of Physics, vol. 81, pp. 417–437, 2013.
  • P. A. Mohammad and H. Feizi, “Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances,” Transactions of the Institute of Measurement and Control, vol. 34, pp. 990–997, 2012.
  • H. R. Koofigar, S. Hosseinnia, and F. Sheikholeslam, “Robust adaptive synchronization of uncertain unified chaotic systems,” Nonlinear Dynamics, vol. 59, no. 3, pp. 477–483, 2010.
  • M. P. Aghababa and A. Heydari, “Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities,” Applied Mathematical Modelling, vol. 36, no. 4, pp. 1639–1652, 2012.
  • P. Liu and S. Liu, “Robust adaptive full state hybrid synchronization of chaotic complex systems with unknown parameters and external disturbances,” Nonlinear Dynamics, vol. 70, no. 1, pp. 585–599, 2012.
  • W. Jawaada, M. S. M. Noorani, and M. M. Al-Sawalha, “Active sliding mode control antisynchronization of chaotic systems with uncertainties and external disturbances,” Journal of Applied Mathematics, vol. 2012, Article ID 293709, 14 pages, 2012.
  • M. P. Aghababa and M. E. Akbari, “A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5757–5768, 2012.
  • T. Kapitaniak, K.-E. Thylwe, I. Cohen, and J. Wojewoda, “Chaos-hyperchaos transition,” Chaos, Solitons & Fractals, vol. 5, no. 10, pp. 2003–2011, 1995.
  • X. Wu, H. Wang, and H. Lu, “Modified generalized projective synchronization of a new fractional-order hyperchaotic system and its application to secure communication,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1441–1450, 2012.
  • M. P. Aghababa, “Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 247–261, 2012.
  • G. Fu, “Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2602–2608, 2012.
  • G. Fu and Z. Li, “Robust adaptive anti-synchronization of two different hyperchaotic systems with external uncertainties,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 395–401, 2011.
  • W. Jawaada, M. S. M. Noorani, and M. M. Al-Sawalha, “Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2403–2413, 2012.
  • Z. Li and X. Zhao, “Generalized function projective synchronization of two different hyperchaotic systems with unknown parameters,” Nonlinear Analysis: Real World Applications, vol. 12, no. 5, pp. 2607–2615, 2011.
  • Z. Yan, “Controlling hyperchaos in the new hyperchaotic Chen system,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1239–1250, 2005.
  • M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, NY, USA, 1995. \endinput