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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 580105, 6 pages
http://dx.doi.org/10.1155/2014/580105
Research Article

Adaptive Control of the Chaotic System via Singular System Approach

1School of Electrical Engineering & Automation, Henan Polytechnic University, Jiaozuo, Henan 454003, China
2School of Mechanical and Electrical Engineering, Henan Vocational College of Industry and Information Technology, Jiaozuo, Henan 454003, China

Received 14 July 2014; Accepted 25 July 2014; Published 12 August 2014

Academic Editor: Weichao Sun

Copyright © 2014 Yudong Li et al. 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. R. Marino and P. Tomei, Nonlinear Control Design: Geometric, Adaptive and Roubust, Prentice Hall, London, UK, 1995.
  2. H. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, USA, 2002.
  3. W. Sun, H. Gao Sr., and O. Kaynak, “Finite frequency H control for vehicle active suspension systems,” IEEE Transactions on Control Systems Technology, vol. 19, no. 2, pp. 416–422, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. W. Sun, Y. Zhao, J. Li, L. Zhang, and H. Gao, “Active suspension control with frequency band constraints and actuator input delay,” IEEE Transactions on Industrial Electronics, vol. 59, no. 1, pp. 530–537, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Sun, H. Gao, and O. Kaynak, “Adaptive backstepping control for active suspension systems with hard constraints,” IEEE/ASME Transactions on Mechatronics, vol. 18, no. 3, pp. 1072–1079, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. C. Wang, N. Pai, and H. Yau, “Chaos control in AFM system using sliding mode control by backstepping design,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 741–751, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Wang, Z. Han, W. Zhang, and Q. Xie, “Synchronization of unified chaotic systems with uncertain parameters based on the CLF,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 715–722, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. C. Wang and H. Yau, “Chaotic analysis and control of microcandilevers with PD feedback using differential transformation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 4, pp. 425–444, 2009. View at Google Scholar · View at Scopus
  10. H. Wang and H. Gu, “Chaotic synchronization in the presence of disturbances based on an orthogonal function neural network,” Asian Journal of Control, vol. 10, no. 4, pp. 470–477, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H. Yau, “Design of adaptive sliding mode controller for chaos synchronization with uncertainties,” Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 341–347, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. L. Liu, Z. Han, and W. Li, “Global sliding mode control and application in chaotic systems,” Nonlinear Dynamics, vol. 56, no. 1-2, pp. 193–198, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Huang, L. Sun, Z. Han, and L. Liu, “Adaptive terminal sliding mode control for nonlinear differential inclusion systems with disturbance,” Nonlinear Dynamics, vol. 72, no. 1-2, pp. 221–228, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. Zhang, X. Liu, and Q. Zhu, “Adaptive chatter free sliding mode control for a class of uncertain chaotic systems,” Applied Mathematics and Computation, vol. 232, pp. 431–435, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. Ma and E. Boukas, “A singular system approach to robust sliding mode control for uncertain Markov jump systems,” Automatica, vol. 45, no. 11, pp. 2707–2713, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C. Wen and C. Cheng, “Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability,” Journal of the Franklin Institute, vol. 345, no. 8, pp. 926–941, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. W. Xiang and F. Chen, “An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 1–9, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. L. Dai, Singular Control Systems, vol. 118 of Lecture Notes in Control and Information Sciences, Springer, Berlin, Germany, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S. Xu and J. Lam, Control and Filtering of Singular Systems, Springer, Berlin, Germany, 2006. View at MathSciNet