Terminal sliding mode control of chaotic Lorenz system: A discrete-time case (original) (raw)

Abstract

The objective of this paper is to design a finite-time controller for Lorenz system in discrete-time. First, a discrete model is derived through the Taylor series expansion. In the next step, a discrete-time terminal sliding mode controller (DTSMC) is developed to reach a finite-time and high precision control. The stability analysis of DTSMC is presented in the presence of external disturbance and model uncertainties. Numerical simulations of Lorenz system are shown and compared with a discrete-time sliding mode control (DSMC) to illustrate the effectiveness of the proposed control scheme.

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References (31)

  1. T. Kapitaniak, "Chaotic oscillations in mechanical systems" New York, Manchester University Press, 1991.
  2. A. Nayfeh, "Applied nonlinear dynamics" New York, Wiley, 1995.
  3. G. Chen, X. Dong, "From chaos to order: methodologies, perspectives and applications" Singapore, World Scientific, 1998.
  4. J. Lu, X. Wu, J. L, "Synchronization of a unified chaotic system and the application in secure communication" Physics Letters A, vol. 305, pp. 365-370, 2002.
  5. S. V. Emelyanov, Variable structure control systems, Nauka, Moscow, 1967.
  6. K. D. Young, V. I. Utkin, U. Uzguner, "A Control Engineer's Guide to Sliding Mode Control" IEEE Trans. On Control System Technology, Vol. 7, No. 3, 1999.
  7. kX. Yu, O. Kaynak, "Sliding-Mode Control With Soft Computing: A Survey" IEEE Trans. On Industrial Electronics, Vol. 56, No. 9, September, 2009.
  8. H. Guo, S. Lin, J. Liu, "A radial basis function sliding mode controller for chaotic Lorenz system" Physics Letters A, 351, pp. 257-261, 2006.
  9. W. Ligang, W. Changhong, "Adaptive fuzzy sliding mode control of Lorenz chaotic system" Front Electr Electron Eng, Vol. 2, No. 3, pp. 277-281, 2007.
  10. H. T. Yau, J. J. Yan, "Design of sliding mode controller for Lorenz chaotic system with nonlinear input" Chaos, Solitons and Fractals, Vol. 19, pp. 891-898, 2004.
  11. J. F. Chang, M. L. Hung, Y. S. Yang, T. L. Liao, J. J. Yan, "Controlling chaos of the family of Rossler systems using sliding mode control" Chaos, Solitons and Fractals, Vol. 37, pp. 609-622, 2008.
  12. M. J. JANG, C. L. CHEN, C. K. CHEN, "SLIDING MODE CONTROL OF CHAOS IN THE CUBIC CHUA'S CIRCUIT SYSTEM" International Journal of Bifurcation and Chaos, Vol. 12, No. 6, pp. 1437-1449, 2002.
  13. L. Hui and J. Li, "Terminal Sliding Mode Control for Spacecraft Formation Flying" IEEE Trans. On Aerospace And Electronic Systems, Vol. 45, No. 3, July, 2009.
  14. R. M. Zhihong and M. O'Day, "A Robust Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators" Journal of Intelligent and Robotic Systems, 24: 23-41, 1999.
  15. H. Wang, Z. Z. Han, Q. Y. Xie, W. Zhang, "Finite-time chaos control via nonsingular terminal sliding mode control" Communications in Nonlinear Science and Numerical Simulation, Vol. 14, pp. 2728-2733, 2009.
  16. Y. Feng, X. Yu and Z. Man, "Non-singular terminal sliding mode control of rigid manipulators" Automatica, 38(12), 2159-2167, July 2002.
  17. L. Yang, J. Yang, "Robust finite-time convergence of chaotic systems via adaptive terminal sliding mode scheme" Communications in Nonlinear Science and Numerical Simulation, Vol. 16, pp. 2405-2413, 2011.
  18. S. Dadras, H. R. Momeni, "Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty" Communications in Nonlinear Science and Numerical Simulation, Vol. 17, pp. 367-377, 2012.
  19. B. Wang, On Discretization of Sliding Mode Control Systems, Ph.D thesis, RMIT University, Melbourne, Australia, 2008.
  20. W. Gao, "Discrete time variable structure control systems" IEEE Trans. On Industrial Electronics, 45:633-637, 1995.
  21. K. Furuta, "Sliding mode control of a discrete system" Systems and Control letters, 14:144-152, 1990.
  22. S. K. Spurgeon, "Hyperplane design techniques for discte-time variable structure control system" Int. J. of Control 55(2), pp. 445- 456, 1992.
  23. S. T. Sarpturk, Y. Istefanopolos and O. Kaynak, "On the stability of Discrete-Time Sliding Mode Control" IEEE Trans. On Automatic Control, Vol.32, No.10, 930-932, October 1987.
  24. A. Bartoszewicz, "Discrete time quasi-sliding-mode-control strategies" IEEE Trans. On Industrial Electronics, 45:633-637, 1998.
  25. G. Monses, discrete time sliding mode control, Ph.D thesis, 2002.
  26. B. Bandyopadhyay, Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach, Springer-Verlag Berlin Heidelberg New York, 2006.
  27. S. Janardhanan and B. Bandyopadhyay,"on discretization of continuous time terminal sliding mode" IEEE Trans. On Automatic Control, Vol. 51, No. 9, pp. 1532-1536, September, 2006.
  28. K. Abidi, J. X. Xu, and J. H. She "A Discrete-Time Terminal Sliding-Mode Control Approach Applied to a Motion Control Problem" IEEE Trans. On Industrial Electronics, Vol. 56, No. 9, September, 2009.
  29. H. Salarieh, S. M. M. Kashani, G. Vossoughi, A. Alasty, "Stabilizing unstable fixed points of discrete chaotic systems via quasi-sliding mode method" Communications in Nonlinear Science and Numerical Simulation, Vol. 14, pp. 839-849, 2009.
  30. K. C. Veluvolu, Y. C. Soh, W. Cao, "Robust discrete-time nonlinear sliding mode state estimation of uncertain nonlinear systems" International Journal of Robust and Nonlinear Control, Vol. 17, pp. 803-828, 2007.
  31. L. Wu, H. Gao, "Sliding mode control of two dimentional systems in rossler model" IET Control Theory and Appl, Vol. 2, No. 4, pp. 352-364, 2008.