Advertisement

Finite-time projective synchronization of fractional-order chaotic systems via soft variable structure control

  • 9 Accesses

Abstract

The finite-time projective synchronization of two fractional-order chaotic systems with control constraints is investigated in this study. A soft variable structure control scheme is first introduced for finite-time synchronization. A controller is then proposed for finite-time generalized projective synchronization. The finite-time stability of the error systems is rigorously proven. The control parameters of the controller are limited by the soft variable structure method considering the constraints of the controller. Finally, numerical simulation results are presented to demonstrate the effectiveness and feasibility of the proposed strategy and verify the theoretical results.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

References

  1. [1]

    J. Hou and R. Xi, The switching fractional order chaotic system and its application to image encryption, Acta Automatica Sinica, 2 (2017) 381–388.

  2. [2]

    J. Zhao, W. Jing and J. Wang, An improved hydraulic valve and its trajectory control of valve spool based on fractional order PI controller, Journal of Mechanical Science and Technology, 32 (6) (2018) 2755–2764.

  3. [3]

    N. M. H. Norsahperi, S. Ahmad, S. F. Toha, I. A. Mahmood and N. H. H. Mohamad Hanif, Robustness analysis of fractional order PID for an electrical aerial platform, Journal of Mechanical Science and Technology, 32 (11) (2018) 5411–5419.

  4. [4]

    M. P. Aghababa and H. P. Aghababa, Chaos synchronization of gyroscopes using an adaptive robust finite-time controller, Journal of Mechanical Science and Technology, 27 (3) (2013) 909–916.

  5. [5]

    A. Ouannas, A. T. Azar and A. Vaidyanathan, A robust method for new fractional hybrid chaos synchronization, Mathematical Methods in the Applied Sciences, 40 (5) (2017) 1804–1812.

  6. [6]

    A. Boulkroune, A. Bouzeriba and T. Bouden, Fuzzy generalized projective synchronization of incommensurate fractionalorder chaotic systems, Neurocomputing, 173 (2016) 606–614.

  7. [7]

    P. Muthukumar, P. Balasubramaniam and K. Ratnavelu, Sliding mode control design for synchronization of fractional order chaotic systems and its application to a new cryptosystem, International Journal of Dynamics and Control, 5 (1) (2017) 115–123.

  8. [8]

    H.-B. Bao and J.-D. Cao, Projective synchronization of fractional- order memristor-based neural networks, Neural Networks, 63 (2015) 1–9.

  9. [9]

    C. Huang, L. Cai and J. Cao, Linear control for synchronization of a fractional-order time-delayed chaotic financial system, Chaos, Solitons & Fractals, 113 (2018) 326–332.

  10. [10]

    K. Rajagopal et al., Fractional order memristor no equilibrium chaotic system with its adaptive sliding mode synchronization and genetically optimized fractional order PID synchronization, Complexity (2017) 1892618.

  11. [11]

    C. Huang and J. Cao, Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system, Physica A: Statistical Mechanics and its Applications, 473 (2017) 262–275.

  12. [12]

    A. Soukkou, A. Boukabou and S. Leulmi, Prediction-based feedback control and synchronization algorithm of fractionalorder chaotic systems, Nonlinear Dynamics, 85 (4) (2016) 2183–2206.

  13. [13]

    S. Shao, M. Chen and X. Yan, Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance, Nonlinear Dynamics, 83 (4) (2016) 1855–1866.

  14. [14]

    M. P. Aghababa, S. Khanmohammadi and G. Alizadeh, Finite- time synchronization of two different chaotic systems with unknown parameters via sliding mode technique, Applied Mathematical Modelling, 35 (6) (2011) 3080–3091.

  15. [15]

    A. Abdurahman, H. Jiang and Z. Teng, Finite-time synchronization for fuzzy cellular neural networks with time-varying delays, Fuzzy Sets and Systems, 297 (2016) 96–111.

  16. [16]

    B. Xin and J. Zhang, Finite-time stabilizing a fractional-order chaotic financial system with market confidence, Nonlinear Dynamics, 79 (2) (2015) 1399–1409.

  17. [17]

    L. Yinghui and Z. Peng, Soft Variable Structure Control Theory and Application, First Ed., National Defence Industry Press, Beijing, China (2014).

  18. [18]

    P. Ignaciuk and M. Morawski, Remote quasi-soft variable structure control of dynamic plants with actuator saturation, 20th International Conference on System Theory, Control and Computing (ICSTCC), Sinaia, Romania (2016) 35–40.

  19. [19]

    M. Kaheni, Z. M. Hadad and K. A. Akbarzadeh, Radial pole paths SVSC for linear time invariant multi input systems with constrained inputs, Asian Journal of Control, 21 (1) (2018) 1–9.

  20. [20]

    M. Kaheni, M. H. Zarif and A. A. Kalat, Soft variable structure control of linear systems via desired pole paths, Journal of Information Technology, 47 (3) (2018) 447–456.

  21. [21]

    S. Kamal and B. Bandyopadhyay, High performance regulator for fractional order systems: A soft variable structure control approach, Asian Journal of Control, 17 (4) (2015) 1342–1346.

  22. [22]

    P. A. Mohammad, K. Sohrab and A. Ghassem, Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique, Applied Mathematical Modelling, 35 (6) (2011) 3080–3091.

  23. [23]

    S. Kamal and B. Bandyopadhyay, Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach, Switzerland: Springer International Publishing, 317 (2015) 129–144.

  24. [24]

    Z. Yige, Y. Wang and Z. Liu, Finite time stability analysis for nonlinear fractional order differential systems, Proceedings of the 32nd Chinese Control Conference, IEEE, Xi’an, China (2013) 487–492.

  25. [25]

    W. Jing and P. Guang, An adaptive sliding mode control for synchronization of fraction order chaotic systems, Acta Phys. Sin., 64 (4) (2015) 40505-1.7.

  26. [26]

    N. Aguila-Camacho, M. A. Duarte-Mermoud and J. A. Gallegos, Lyapunov functions for fractional order systems, Communications in Nonlinear Science and Numerical Simulation, 19 (9) (2014) 2951–2957.

Download references

Author information

Correspondence to Keyong Shao.

Additional information

Recommended by Editor Ja Choon Koo

Keyong Shao is currently a Professor at the School of Electrical and Information Engineering, Northeast Petroleum University. He was born in Huaiyang, Henan Province, China in 1970. He received his B.S. degree from Daqing Northeast Petroleum Institute in 1992, his M.S. degree from Northeast University, Shenyang, China in 2000, and his Ph.D. in Control Theory and Control Engineering from Northeast University, Shenyang, China in 2003. His main research interests include robust control and fractional-order system theory.

Haoxuan Guo received his B.S. and M.S. degrees in Control Theory and Control Engineering from Northeast Petroleum University, China in 2012 and 2019, respectively. His main research interests include soft variable structure control and fractional-order system theory.

Feng Han received his B.S. and M.S. degrees in Control Theory and Control Engineering from Northeast Petroleum University, China in 2012 and 2018, respectively. His main research interests include sliding-mode control and fractional- order system theory

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shao, K., Guo, H. & Han, F. Finite-time projective synchronization of fractional-order chaotic systems via soft variable structure control. J Mech Sci Technol 34, 369–376 (2020). https://doi.org/10.1007/s12206-019-1236-7

Download citation

Keywords

  • Fractional-order chaotic systems
  • Chaos synchronization
  • Soft variable structure control
  • Projective synchronization