Table of Contents Author Guidelines Submit a Manuscript
Applied Computational Intelligence and Soft Computing
Volume 2014 (2014), Article ID 613463, 9 pages
http://dx.doi.org/10.1155/2014/613463
Research Article

Lyapunov-Based Controller for a Class of Stochastic Chaotic Systems

Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 5166614776, Iran

Received 25 July 2014; Accepted 4 November 2014; Published 10 December 2014

Academic Editor: Zhang Yi

Copyright © 2014 Hossein Shokouhi-Nejad 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. J. A. Gallegos, “Nonlinear regulation of a Lorenz system by feedback linearization techniques,” Dynamics and Control, vol. 4, no. 3, pp. 277–298, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. A. Razminia and D. F. M. Torres, “Control of a novel chaotic fractional order system using a state feedback technique,” Mechatronics, vol. 23, no. 7, pp. 755–763, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Dadras, H. R. Momeni, and V. J. Majd, “Sliding mode control for uncertain new chaotic dynamical system,” Chaos, Solitons and Fractals, vol. 41, no. 4, pp. 1857–1862, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. S. Dadras and H. R. Momeni, “Control of a fractional-order economical system via sliding mode,” Physica A: Statistical Mechanics and Its Applications, vol. 389, no. 12, pp. 2434–2442, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Li, W. Li, and Q. Li, “Sliding mode control for uncertain chaotic systems with input nonlinearity,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 341–348, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. M. Roopaei, B. R. Sahraei, and T.-C. Lin, “Adaptive sliding mode control in a novel class of chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4158–4170, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Yuan, B. Shi, and W. Ji, “Adaptive sliding mode control of a novel class of fractional chaotic systems,” Advances in Mathematical Physics, vol. 2013, Article ID 576709, 13 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. Layeghi, M. T. Arjmand, H. Salarieh, and A. Alasty, “Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control,” Chaos, Solitons and Fractals, vol. 37, no. 4, pp. 1125–1135, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. D. Sadaoui, A. Boukabou, and S. Hadef, “Predictive feedback control and synchronization of hyperchaotic systems,” Applied Mathematics and Computation, vol. 247, pp. 235–243, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C. Wu, Y. Lei, and T. Fang, “Stochastic chaos in a Duffing oscillator and its control,” Chaos, Solitons and Fractals, vol. 27, no. 2, pp. 459–469, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. M. Pascual and P. Mazzega, “Quasicycles revisited: apparent sensitivity to initial conditions,” Theoretical Population Biology, vol. 64, no. 3, pp. 385–395, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. W. J. Freeman, “A proposed name for aperiodic brain activity: stochastic chaos,” Neural Networks, vol. 13, no. 1, pp. 11–13, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. P. R. Patnaik, “The extended Kalman filter as a noise modulator for continuous yeast cultures under monotonic, oscillating and chaotic conditions,” Chemical Engineering Journal, vol. 108, no. 1-2, pp. 91–99, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. N. Kikuchi, Y. Liu, and J. Ohtsubo, “Chaos control and noise suppression in external-cavity semiconductor lasers,” IEEE Journal of Quantum Electronics, vol. 33, no. 1, pp. 56–65, 1997. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Kyrtsou and M. Terraza, “Stochastic chaos or ARCH effects in stock series? A comparative study,” International Review of Financial Analysis, vol. 11, no. 4, pp. 407–431, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, Berlin, Germany, 3rd edition, 1992.
  17. H. Salarieh and A. Alasty, “Control of stochastic chaos using sliding mode method,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 135–145, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. S. A. Poznyak, Advanced Mathematical Tools for Automatic control Engineers, Elsevier, 2009.
  19. X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK, 1997.
  20. L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York, NY, USA, 1972.
  21. A. Friedman, Stochastic Differential Equations and Applications, vol. 1, Academic Press, New York, NY, USA, 1975. View at MathSciNet
  22. S. Xu, P. Shi, F. Chunmei, G. Yiqian, and Z. Yun, “Robust observers for a class of uncertain nonlinear stochastic systems with state delays,” Nonlinear Dynamics and Systems Theory, vol. 4, no. 3, pp. 369–380, 2004. View at Google Scholar
  23. Y. Chen, A. Xue, S. Zhou, and R. Lu, “Delay-dependent robust control for uncertain stochastic time-delay systems,” Circuits, Systems, and Signal Processing, vol. 27, no. 4, pp. 447–460, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus