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Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3353–3363 | Cite as

Bounded Scaling Function Projective Synchronization of Chaotic Systems with Adaptive Finite-Time Control

  • Yuhua Xu
  • Wuneng Zhou
  • Chengrong Xie
Article

Abstract

This paper investigates the bounded scaling function projective synchronization of uncertain chaotic systems using adaptive finite-time control. Based on finite-time control and inequality principle, the new adaptive finite-time controller is designed to achieve two chaotic systems scaling function projective synchronized, and uncertain parameters of chaotic systems are also identified. Moreover, in comparison with those of the existing scaling function synchronization, the given scaling function can be more complex bounded functions. Some numerical are also given to show the effectiveness of the proposed method.

Keywords

Chaotic system Projective synchronization Adaptive synchronization Finite-time control 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61673221, 61673257, and 11701287), the Youth Fund Project of the Humanities and Social Science Research for the Ministry of Education of China (14YJCZH173), Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (Jiangsu Province Office, No. [2015]1, PPZY2015B104), the Key Laboratory of Financial Engineering of Jiangsu Province (NSK2015-16), Applied Economics of key Sequence Disciplines of Jiangsu Higher Education Institutions (Jiangsu Province Office, No. [2014]37), “Qing-Lan Engineering” Foundation of Jiangsu Higher Education Institutions, and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

References

  1. 1.
    S.P. Bhat, D.S. Bernstein, Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(11), 678–682 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    G.R. Chen, T. Ueta, Yet another chaotic attractor. Int. J. Bifur. Chaos 9, 1465–1466 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    S. Dadras, H.R. Momeni, Adaptive sliding mode control of chaotic dynamical systems with application to synchronization. Math. Comput. Simul. 80(12), 2245–2257 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S. Dadras, H.R. Momeni, V.J. Majd, Sliding mode control for uncertain new chaotic dynamical system. Chaos Solitons Fract. 41(4), 1857–1862 (2009)CrossRefzbMATHGoogle Scholar
  5. 5.
    Z.X. Ding, Y. Shen, Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller. Neural Netw. 76, 97–105 (2016)CrossRefGoogle Scholar
  6. 6.
    A.G. Ghada, M.S.N. Noorani, S.A. Bakar, S. Vahedi, Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance. Neurocomputing 207, 645–652 (2016)CrossRefGoogle Scholar
  7. 7.
    S.P. He, F. Liu, Robust finite-time stabilization of uncertain fuzzy jump systems. Int. J. Innov. Comput. Inf. Control 9, 3853–3862 (2010)Google Scholar
  8. 8.
    G.Z. Hu, Global synchronization for coupled Lur’e dynamical networks. Circuits Syst. Signal Process. 32(6), 2851–2866 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    G. Hardy, J.E. Littlewood, G. Polya, Inequalities (Cambridge University Press, Cambridge, 1952)zbMATHGoogle Scholar
  10. 10.
    T.Y. Jing, F.Q. Chen, X.H. Zhang, Finite-time lag synchronization of time-varying delayed complex networks via periodically intermittent control and sliding mode control. Neurocomputing 199, 178–184 (2016)CrossRefGoogle Scholar
  11. 11.
    J.Q. Lu, Z.D. Wang, J.D. Cao, D.W.C. Ho, J. Kurths, Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int. J. Bifur. Chaos 22(7), 1250176 (2012)CrossRefzbMATHGoogle Scholar
  12. 12.
    J.Q. Lu, J. Kurths, J.D. Cao, N. Mahdavi, C. Huang, Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 285–292 (2012)CrossRefGoogle Scholar
  13. 13.
    J.Q. Lu, C.D. Ding, J.G. Lou, J.D. Cao, Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J. Frankl. Inst. 352, 5024–5041 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    R.Q. Lu, P. Shi, H.Y. Su, Z.G. Wu, J.H. Lü, Synchronization of general chaotic neural networks with non-uniform sampling and packet missing: a switched system approach. IEEE Trans. Neural Netw. Learn. Syst. (2016).  https://doi.org/10.1109/TNNLS.2016.2636163 Google Scholar
  15. 15.
    T.H. Lee, J.H. Park, S.Y. Xu, Relaxed conditions for stability of time-varying delay systems. Automatica 75, 11–15 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    T.H. Lee, J.H. Park, A novel Lyapunov functional for stability of time-varying delay systems via matrix refined-function. Automatica 80, 239–242 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    J.H. Lü, G.R. Chen, A new chaotic attractor coined. Int. J. Bifur. Chaos 12, 659–661 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Y.C. Ma, N.N. Ma, Finite-time H\(\infty \) synchronization for complex dynamical networks with mixed mode-dependent time delays. Neurocomputing 218, 223–233 (2016)CrossRefGoogle Scholar
  19. 19.
    G.F. Mei, X.Q. Wu, D. Ning, J.A. Lu, Finite-time stabilization of complex dynamical networks via optimal control. Complexity 21, 417–425 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    R. Rakkiyappan, N. Sakthivel, J.D. Cao, Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Neural Netw. 66, 46–63 (2015)CrossRefGoogle Scholar
  21. 21.
    L. Shi, H. Zhu, S.M. Zhong, K.B. Shi, J. Cheng, Function projective synchronization of complex networks with asymmetric coupling via adaptive and pinning feedback control. ISA Trans. 65, 81–87 (2016)CrossRefGoogle Scholar
  22. 22.
    H. Shen, J.H. Park, Z.G. Wu, Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn. 77(4), 1709–1720 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Y. Tang, W.K. Wong, Distributed synchronization of coupled neural networks via randomly occurring control. IEEE Trans. Neural Netw. Learn. Syst. 24, 435–447 (2013)CrossRefGoogle Scholar
  24. 24.
    Y. Tang, H.J. Gao, W. Zou, J. Kurths, Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Trans. Cybern. 43, 358–370 (2013)CrossRefGoogle Scholar
  25. 25.
    Y.Q. Wu, R.Q. Lu, P. Sh, H.Y. Su, Z.G. Wu, Adaptive output synchronization of heterogeneous network with an uncertain leader. Automatica 76, 183–192 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Y.Q. Wu, X. Meng, L.H. Xie, R.Q. Lu, H.Y. Su, An input-based triggering approach to leader-following problems. Automatica 75, 221–228 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Y.Q. Wu, H.Y. Su, P. Shi, R.Q. Lu, Z.G. Wu, Output synchronization of non-identical linear multi-agent systems. IEEE Trans. Cybern. 47(1), 130–141 (2017)CrossRefGoogle Scholar
  28. 28.
    Y.Q. Wu, H.Y. Su, Z.G. Wu, Asymptotical synchronization of chaotic Lur’e systems under time-varying sampling. Circuits Syst. Signal Process. 33(3), 699–712 (2014)CrossRefGoogle Scholar
  29. 29.
    E.L. Wu, X.S. Yang, Generalized lag synchronization of neural networks with discontinuous activations and bounded perturbations. Circuits Syst. Signal Process. 34(7), 2381–2394 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    X. Wang, J.A. Fang, H.Y. Mao, A.D. Dai, Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control. Nonlinear Dyn. 79, 47–61 (2015)CrossRefzbMATHGoogle Scholar
  31. 31.
    J.K. Wang, X.Q. Chen, J.K. Fu, Adaptive finite-time control of chaos in permanent magnet synchronous motor with uncertain parameters. Nonlinear Dyn. 78(2), 1321–1328 (2014)CrossRefzbMATHGoogle Scholar
  32. 32.
    Y. Wu, Y.H. Sun, L.F. Chen, Robust adaptive finite-time synchronization of nonlinear resource management system. Neurocomputing 171, 1131–1138 (2016)CrossRefGoogle Scholar
  33. 33.
    Y.W. Wang, W. Yang, J.W. Xiao, Z.G. Zeng, Impulsive multi-synchronization of coupled multistable neural networks with time-varying delay. IEEE Trans. Neural Netw. Learn. Syst. 28(7), 1560–1571 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Y.H. Xu, W.N. Zhou, J.A. Fang, Modified scaling function projective synchronization of chaotic systems. Chin. Phys. B. 20(9), 090509 (2011)CrossRefGoogle Scholar
  35. 35.
    Y.H. Xu, W.N. Zhou, J.A. Fang, C.R. Xie, D.B. Tong, Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling. Neurocomputing 173, 1356–1361 (2016)CrossRefGoogle Scholar
  36. 36.
    Y.H. Xu, Y.J. Lu, W.X. Yan, W.N. Zhou, J.A. Fang, Bounded synchronization of the general complex dynamical network with delay feedback controller. Nonlinear Dyn. 84, 661–667 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    L.W. Zhou, Z.J. Wang, J. Zhou, W.N. Zhou, Mean square synchronization of neural networks with Levy noise via sampled-data and actuator saturating controller. Neurocomputing 173, 1235–1244 (2016)CrossRefGoogle Scholar
  38. 38.
    H. Zhang, Q.Q. Hong, H.C. Yan, F.W. Yang, G. Guo, Event-based distributed H\(\infty \) filtering networks of 2DOF quarter-car suspension systems. IEEE Trans. Ind. Inform. 13(1), 312–321 (2017)CrossRefGoogle Scholar
  39. 39.
    H. Zhang, X.Y. Zheng, H.C. Yan, C. Peng, Z.P. Wang, Q.J. Chen, Codesign of event-triggered and distributed H\(\infty \) filtering for active semi-vehicle suspension systems. IEEE Trans. Mechatron. 22(2), 1047–1058 (2017)CrossRefGoogle Scholar
  40. 40.
    H. Zhang, R.H. Yang, H.C. Yan, F.W. Yang, H\(\infty \) consensus of event-based multi-agent systems with switching topology. Inf. Sci. 370, 623–635 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of FinanceNanjing Audit UniversityNanjingChina
  2. 2.College of Information Science and TechnologyDonghua UniversityShanghaiChina
  3. 3.College of ScienceNanjing Audit UniversityNanjingChina

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