Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2018, Article ID 3545083, 9 pages
https://doi.org/10.1155/2018/3545083
Research Article

Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

College of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China

Correspondence should be addressed to Chenhui Wang; nc.ude.tumx@gnawhc

Received 5 October 2017; Revised 19 December 2017; Accepted 20 December 2017; Published 17 January 2018

Academic Editor: Christos Volos

Copyright © 2018 Chenhui Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Liu, S.-G. Li, Y.-G. Sun, and H.-X. Wang, “Adaptive fuzzy synchronization for uncertain fractional-order chaotic systems with unknown non-symmetrical control gain,” Wuli Xuebao/Acta Physica Sinica, vol. 64, no. 7, Article ID 070503, 2015. View at Publisher · View at Google Scholar · View at Scopus
  2. H. Liu, S. Li, Y. Sun, and H. Wang, “Prescribed performance synchronization for fractional-order chaotic systems,” Chinese Physics B, vol. 24, no. 9, Article ID 090505, 2015. View at Publisher · View at Google Scholar
  3. S. Vaidyanathan and S. Pakiriswamy, “A five-term 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control method,” Control Theory and Technology, vol. 9, no. 1, pp. 61–78, 2016. View at Google Scholar · View at Scopus
  4. C. Volos, V.-T. Pham, E. Zambrano-Serrano, J. M. Munoz-Pacheco, S. Vaidyanathan, and E. Tlelo-Cuautle, “Analysis of a 4-D hyperchaotic fractional-order memristive system with hidden attractors,” in Advances in Memristors, Memristive Devices and Systems, vol. 701, pp. 207–235, Springer, 2017. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Volos, S. Vaidyanathan, V.-T. Pham et al., “Adaptive control and synchronization of a memristor-based Shinriki’s system,” in Advances in Memristors, Memristive Devices and Systems, vol. 701, pp. 237–261, Springer, 2017. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Ouannas, Z. Odibat, N. Shawagfeh, A. Alsaedi, and B. Ahmad, “Universal chaos synchronization control laws for general quadratic discrete systems,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 45, pp. 636–641, 2017. View at Google Scholar · View at MathSciNet
  7. A. Ouannas and Z. Odibat, “On inverse generalized synchronization of continuous chaotic dynamical systems,” International Journal of Applied and Computational Mathematics, vol. 2, no. 1, pp. 1–11, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. Boulkroune, A. Bouzeriba, T. Bouden, and A. T. Azar, “Fuzzy adaptive synchronization of uncertain fractional-order chaotic systems,” in Advances in chaos theory and intelligent control, vol. 337, pp. 681–697, Springer, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Boulkroune, A. Bouzeriba, and T. Bouden, “Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems,” Neurocomputing, vol. 173, pp. 606–614, 2016. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Çiçek, A. Ferikoglu, and I. Pehlivan, “A new 3D chaotic system: dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 8, pp. 4024–4030, 2016. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Vaidyanathan and A. T. Azar, “Dynamic analysis, adaptive feedback control and synchronization of an eight-term 3-D novel chaotic system with three quadratic nonlinearities,” in Advances in Chaos Theory and Intelligent Control, vol. 337, pp. 155–178, Springer, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Sampath and S. Vaidyanathan, “Hybrid synchronization of identical chaotic systems via novel sliding control method with application to Sampath four-scroll chaotic system,” Control Theory and Technology, vol. 9, no. 1, pp. 221–235, 2016. View at Google Scholar · View at Scopus
  13. 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, vol. 5, no. 1, pp. 115–123, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. H. Liu, S. Li, H. Wang, Y. Huo, and J. Luo, “Adaptive synchronization for a class of uncertain fractional-order neural networks,” Entropy, vol. 17, no. 10, pp. 7185–7200, 2015. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Liu, Y. Pan, S. Li, and Y. Chen, “Synchronization for fractional-order neural networks with full/under-actuation using fractional-order sliding mode control,” International Journal of Machine Learning and Cybernetics, pp. 1–14, 2017. View at Publisher · View at Google Scholar
  16. H. Liu, S.-G. Li, H.-X. Wang, and G.-J. Li, “Adaptive fuzzy synchronization for a class of fractional-order neural networks,” Chinese Physics B, vol. 26, no. 3, Article ID 030504, 2017. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Li, J. Yu, C. Hilton, and H. Liu, “Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach,” IEEE Transactions on Industrial Electronics, vol. 60, no. 8, pp. 3328–3338, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Pan and H. Yu, “Composite learning from adaptive dynamic surface control,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 61, no. 9, pp. 2603–2609, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. H. Li, P. Shi, and D. Yao, “Adaptive sliding mode control of markov jump nonlinear systems with actuator faults,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 1933–1939, 2016. View at Publisher · View at Google Scholar
  20. H. Wang, “Core-EP decomposition and its applications,” Linear Algebra and Its Applications, vol. 508, pp. 289–300, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  21. H. Wang and X. Liu, “A partial order on the set of complex matrices with index one,” Linear and Multilinear Algebra, pp. 1–11, 2017. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Liu, S. Vazquez, L. Wu, A. Marquez, H. Gao, and L. G. Franquelo, “Extended State Observer-Based Sliding-Mode Control for Three-Phase Power Converters,” IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 22–31, 2017. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Pan, C. Yang, L. Pan, and H. Yu, “Integral Sliding Mode Control: Performance, Modification and Improvement,” IEEE Transactions on Industrial Informatics, 2017. View at Publisher · View at Google Scholar
  24. H. Wang and W. Guo, “The minimal rank of matrix expressions with respect to Hermitian matrix-revised,” Journal of The Franklin Institute, vol. 353, no. 5, pp. 1206–1219, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. H. Komurcugil and S. Biricik, “Time-Varying and Constant Switching Frequency-Based Sliding-Mode Control Methods for Transformerless DVR Employing Half-Bridge VSI,” IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 2570–2579, 2017. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Pan, H. Wang, X. Li, and H. Yu, “Adaptive Command-Filtered Backstepping Control of Robot Arms With Compliant Actuators,” IEEE Transactions on Control Systems Technology, pp. 1–8, 2017. View at Publisher · View at Google Scholar
  27. Y. Pan, Z. Guo, X. Li, and H. Yu, “Output-feedback adaptive neural control of a compliant differential SMA actuator,” IEEE Transactions on Control Systems Technology, vol. 25, no. 6, pp. 2202–2210, 2017. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Yin, S. Dadras, S.-M. Zhong, and Y. Chen, “Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach,” Applied Mathematical Modelling, vol. 37, no. 4, pp. 2469–2483, 2013. View at Publisher · View at Google Scholar · View at Scopus
  29. C. Yin, Y. Cheng, S.-M. Zhong, and Z. Bai, “Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems,” Complexity, vol. 21, no. 6, pp. 363–373, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. A. Mohammadzadeh and S. Ghaemi, “A modified sliding mode approach for synchronization of fractional-order chaotic/hyperchaotic systems by using new self-structuring hierarchical type-2 fuzzy neural network,” Neurocomputing, vol. 191, pp. 200–213, 2016. View at Publisher · View at Google Scholar · View at Scopus
  31. J. Shen and J. Lam, “Non-existence of finite-time stable equilibria in fractional-order nonlinear systems,” Automatica, vol. 50, no. 2, pp. 547–551, 2014. View at Publisher · View at Google Scholar · View at Scopus
  32. J. C. Trigeassou, N. Maamri, J. Sabatier, and A. Oustaloup, “A Lyapunov approach to the stability of fractional differential equations,” Signal Processing, vol. 91, no. 3, pp. 437–445, 2011. View at Publisher · View at Google Scholar · View at Scopus
  33. D. Matignon, “Stability result for fractional differential equations with applications to control processing,” in Computational Engineering in Systems Applications, pp. 963–968, IMACS, IEEE-SMC, Lille, France, 1997. View at Google Scholar
  34. J.-G. Lu and G. Chen, “Robust stability and stabilization of fractional-order interval systems: an LMI approach,” IEEE Transactions on Automatic Control, vol. 54, no. 6, pp. 1294–1299, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  35. Y. Li, Y. Chen, and I. Podlubny, “Mittag-Leffler stability of fractional order nonlinear dynamic systems,” Automatica, vol. 45, no. 8, pp. 1965–1969, 2009. View at Publisher · View at Google Scholar · View at Scopus
  36. H. Delavari, D. Baleanu, and J. Sadati, “Stability analysis of Caputo fractional-order nonlinear systems revisited,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2433–2439, 2012. View at Publisher · View at Google Scholar · View at Scopus
  37. X.-J. Wen, Z.-M. Wu, and J.-G. Lu, “Stability analysis of a class of nonlinear fractional-order systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, no. 11, pp. 1178–1182, 2008. View at Publisher · View at Google Scholar · View at Scopus
  38. S. Liu, W. Jiang, X. Li, and X.-F. Zhou, “Lyapunov stability analysis of fractional nonlinear systems,” Applied Mathematics Letters, vol. 51, pp. 13–19, 2016. View at Publisher · View at Google Scholar · View at Scopus
  39. X. Yang, C. Li, T. Huang, and Q. Song, “Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses,” Applied Mathematics and Computation, vol. 293, pp. 416–422, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  40. H. Liu, S. Li, J. D. Cao, A. G. Alsaedi, and F. E. Alsaadi, “Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances,” Neurocomputing, vol. 219, pp. 422–430, 2017. View at Publisher · View at Google Scholar
  41. H. Liu, Y. Pan, S. Li, and Y. Chen, “Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2209–2217, 2017. View at Publisher · View at Google Scholar
  42. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  43. L. Chen, Y. Chai, R. Wu, and J. Yang, “Stability and stabilization of a class of nonlinear fractional-order systems with caputo derivative,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 9, pp. 602–606, 2012. View at Publisher · View at Google Scholar · View at Scopus
  44. H. Liu, S. Li, G. Li, and H. Wang, “Adaptive Controller Design for a Class of Uncertain Fractional-Order Nonlinear Systems: An Adaptive Fuzzy Approach,” International Journal of Fuzzy Systems, pp. 1–14, 2017. View at Publisher · View at Google Scholar
  45. I. Petráš, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer Science & Business Media, 2011.
  46. Z. M. Ge and C. Y. Ou, “Chaos in a fractional order modified Duffing system,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 262–291, 2007. View at Publisher · View at Google Scholar · View at Scopus