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Adaptive Fuzzy Synchronization for Uncertain Chaotic Systems with Different Dimensions and Disturbances

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Abstract

This paper focuses on the design of a novel adaptive fuzzy controller to synchronize the uncertain master–slave chaotic systems with different dimensions. In this paper, completely unknown nonlinear structures and disturbances exist in both the master and slave systems. For such systems, the definition of the generalized linear master–slave synchronization (GLMSS) is proposed. And different from the existing literatures, it is the unknown norm bound function of the uncertain structure to be approximated by the fuzzy logic system. Thus, regardless of the number of the nonlinear functions in the master and slave systems’ unknown structures, only two fuzzy logic systems are needed to synthesize the adaptive controller which guarantees the two systems achieving GLMSS. Three numerical examples are given to verify the effectiveness and feasibility of the fuzzy adaptive control scheme in this paper.

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References

  1. Chen, G., Dong, X.: From chaos to order: methodologies, perspectives and applications. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  2. Motallebzadeh, F., Motlagh, M.R.J., Cherati, Z.R.: Synchronization of different-order chaotic systems: adaptive active versus optimal control. Commun. Nonlinear Sci. Numer. Simul. 17, 3643–3657 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model. 35, 3080–3091 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kim, J.H., Park, C.W., Kim, E., Park, M.: Fuzzy adaptive synchronization for uncertain chaotic systems. Phys. Lett. A 334, 295–305 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Wang, Y.H., Fan, Y.Q., Wang, Q.Y., Zhang, Y.: Adaptive fuzzy synchronization for a class of chaotic systems with unknown nonlinearities and disturbances. Nonlinear Dyn. 69, 1167–1176 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hu, M.F., Xu, Z.Y., Zhang, R., Hu, A.H.: Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems. Phys. Lett. A 361, 231–237 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Adaptive fuzzy tracking control of nonlinear MIMO systems with time-varying delays. Fuzzy Sets Syst. 217, 1–21 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lin, T.C., Lee, T.Y., Balas, V.E.: Adaptive fuzzy sliding control for synchronization of uncertain fractional order chaotic systems. Chaos Solitons Fractals 44, 780–791 (2011)

    Google Scholar 

  9. Li, S.Y., Ge, Z.M.: Generalized synchronization of chaotic systems with different orders by fuzzy logic constant controller. Expert Syst. Appl. 38, 2302–2310 (2011)

    Article  Google Scholar 

  10. Li, S.Y., Yang, C.H., Chen, S.A., Ko, L.W., Lin, C.T.: Fuzzy adaptive synchronization of time-reversed chaotic systems via a new adaptive control strategy. Inf. Sci. 222, 486–500 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  11. Yau, H.T., Shieh, C.S.: Chaos synchronization using fuzzy logic controller. Nonlinear Anal. 9, 1800–1810 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Terman, D., Kopell, N., Bose, A.: Dynamics of two mutually coupled slow inhibitory neurons. Physica D 117, 241–275 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Schäfer, C., Rosenblum, M.G., Abel, H.H., Kurths, J.R.: Synchronization in the human cardiorespiratory system. Phys. Rev. E 60, 857–870 (1999)

    Article  Google Scholar 

  14. Hu, M.F., Xu, Z.Y., Zhang, R., Hu, A.H.: Adaptive full state hybrid projective synchronization of chaotic systems with the same and different order. Phys. Lett. A 365, 315–327 (2007)

    Article  MathSciNet  Google Scholar 

  15. Alvarez, G., Hernández, L., Muñoz, J., Montoya, F., Li, S.J.: Security analysis of communication system based on the synchronization of different order chaotic systems. Phys. Lett. A 345, 245–250 (2005)

    Article  MATH  Google Scholar 

  16. Bowong, S.: Stability analysis for the synchronization of chaotic systems with different order: application to secure communications. Phys. Lett. A 326, 102–113 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Cai, N., Li, W.Q., Jing, Y.W.: Finite-time generalized synchronization of chaotic systems with different order. Nonlinear Dyn. 64, 385–393 (2011)

    Article  MathSciNet  Google Scholar 

  18. Ge, Z.M., Yang, C.H.: The generalized synchronization of a Quantum-CNN chaotic oscillator with different order systems. Chaos Solitons Fractals 35, 980–990 (2008)

    Article  MATH  Google Scholar 

  19. Zhang, G., Liu, Z.R., Ma, Z.J.: Generalized synchronization of different dimensional chaotic dynamical systems. Chaos Solitons Fractals 32, 773–779 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ricardo, F., Gualberto, S.P.: Synchronization of chaotic systems with different order. Phys Rev E 65, 036226-1–036226-7 (2002)

    Google Scholar 

  21. Laoye, J.A., Vincent, U.E., Akigbogun, O.O.: Chaos control and reduced-order synchronization of the rigid body. Int. J. Nonlinear Sci. 6, 106–113 (2008)

    MATH  MathSciNet  Google Scholar 

  22. Ge, Z.M., Chang, C.M., Chen, Y.S.: Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems. Chaos Solitons Fractals 27, 1298–1315 (2006)

    Article  MATH  Google Scholar 

  23. Rodríguez, A., León, J.D., Fridman, L.: Quasi-continuous high-order sliding-mode controllers for reduced-order chaos synchronization. Int. J. Non-Linear Mech. 43, 948–961 (2008)

    Article  Google Scholar 

  24. Vincent, U.E., Guo, R.W.: A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 14, 3925–3932 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. Xu, W., Yang, X.L., Sun, Z.K.: Full- and reduced-order synchronization of a class of time-varying systems containing uncertainties. Nonlinear Dyn. 52, 19–25 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Noroozi, N., Roopaei, M., Jahromi, M.Z.: Adaptive fuzzy sliding mode control scheme for uncertain systems. Commun. Nonlinear Sci. Numer. Simul. 14, 3978–3992 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. Chen, L., Chen, G.R., Lee, Y.W.: Fuzzy modeling and adaptive control of uncertain chaotic systems. Inf. Sci. 121, 27–37 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Wang, L.X., Mendel, J.M.: Fuzzy basis functions, universal approximation and orthogonal least squares learning. IEEE Trans. Neural Netw. 3, 807–814 (1992)

    Article  Google Scholar 

  29. Ying, H.: General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators. IEEE Trans. Fuzzy Syst. 6, 582–587 (1998)

    Article  Google Scholar 

  30. Guan, X.P., Chen, C.L.: Adaptive fuzzy control for chaotic systems with H ∞ tracking performance. Fuzzy Sets Syst. 139, 81–93 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  31. Chen, B., Liu, X.P., Tong, S.C.: Adaptive fuzzy approach to control unified chaotic systems. Chaos Solitons Fractals 34, 1180–1187 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Fan, Y.Q., Wang, Y.H., Wang, W.Q.: Adaptive fuzzy tracking control with compressor and limiters for uncertain nonlinear systems. Int. J. Fuzzy Syst. 16, 31–38 (2014)

    Google Scholar 

  33. Liu, Z., Wang, F., Zhang, Y., Chen, X., Philip Chen, C.L.: Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach. IEEE Trans. Cybern. 44, 1714–1725 (2014)

    Article  Google Scholar 

  34. Wang, H., Chen, B., Lin, C.: Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input. Int. J. Syst. Sci. 45, 2552–2564 (2014)

    Article  MathSciNet  Google Scholar 

  35. Yu, Y.G., Li, H.X.: Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design. Nonlinear Anal. 12, 388–393 (2011)

    Article  MATH  Google Scholar 

  36. Chen, J., Liu, H., Lu, J.A., Zhang, Q.J.: Projective and lag synchronization of a novel hyperchaotic system via impulsive control. Commu. Nonlinear Sci. Numer. Simul. 16, 2033–2040 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  37. Wang, Y.H., Fan, Y.Q., Wang, Q.Y., Zhang, Y.: Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers. IEEE Trans. Circuits Syst.-I 59, 1786–1795 (2012)

    Article  MathSciNet  Google Scholar 

  38. Slotine, J.J.E., Li, W.: Applied nonlinear control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  39. Yan, Z.Y.: Controlling hyperchaos in the new hyper-chaotic Chen system. Appl. Math. Comput. 168, 1239–1250 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  40. Jia, Q.: Projective synchronization of a new hyperchaotic Lorenz system. Phys. Lett. A 370, 40–45 (2007)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China (61273219), the National Science Foundation of Guangdong Province of China (S2013010015768, S2012040007700), Project Program of KLGHEI of China (2013CXZDA015), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20134420110003), and the Important Program for Young Scientists of Guangdong University of Technology (2014).

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Authors and Affiliations

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, China

    Lili Zhang

  2. School of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Lili Zhang, Yinhe Wang & Qinruo Wang

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  1. Lili Zhang
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  2. Yinhe Wang
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  3. Qinruo Wang
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Correspondence to Lili Zhang.

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Zhang, L., Wang, Y. & Wang, Q. Adaptive Fuzzy Synchronization for Uncertain Chaotic Systems with Different Dimensions and Disturbances. Int. J. Fuzzy Syst. 17, 309–320 (2015). https://doi.org/10.1007/s40815-015-0014-7

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  • DOI: https://doi.org/10.1007/s40815-015-0014-7

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