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Chaos Suppression in forced Van Der Pol Oscillator

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International Journal of Computer Applications
© 2013 by IJCA Journal
Volume 68 - Number 23
Year of Publication: 2013
Authors:
Mchiri Mohamed
Trabelsi Karim
Safya Belghith
10.5120/11719-7388

Mchiri Mohamed, Trabelsi Karim and Safya Belghith. Article: Chaos Suppression in forced Van Der Pol Oscillator. International Journal of Computer Applications 68(23):18-23, April 2013. Full text available. BibTeX

@article{key:article,
	author = {Mchiri Mohamed and Trabelsi Karim and Safya Belghith},
	title = {Article: Chaos Suppression in forced Van Der Pol Oscillator},
	journal = {International Journal of Computer Applications},
	year = {2013},
	volume = {68},
	number = {23},
	pages = {18-23},
	month = {April},
	note = {Full text available}
}

Abstract

This paper presents a new method of controlling chaos in the nonlinear Van Der Pol oscillator with uncertainties. The proposed method is based on a nonlinear observer to estimate unmeasured velocity signal coupled to a control law. The observer ensures, firstly, an asymptotic convergence of the velocity estimation error. Then, the control law, which is based on the estimated variables, forces the output system to track a desired trajectory despite presence of uncertainties (external forces) on the system dynamics. Simulation results are provided to show the effectiveness of the proposed control strategy.

References

  • Ott E. , C. Grebogi, J. A. Yorke. 1990. Controlling chaos, Physical Review Letters, vol. 64, 1196–1200.
  • Xu Y. L. , W. L. Qu, B. Chen. 2003. Active/robust moment controllers for seismic response control of a large span building on top of ship lift towers. Journal of Sound and Vibration, vol. 261, 277–296.
  • Dong, X. , G. Chen, L. Chen. 1997. Controlling the uncertain Duffing oscillator", In Proceedings of the First International Conference on Control Oscillation and Chaos, 1997, vol. 2, pp 419–422.
  • Fradkov A. , A. Pogromsky, A. Yu. 1996. Introduction to Control of Oscillations and Chaos. World Scientific, Singapore.
  • Guo C. X. , Q. Y. Jiang, Y. J. Cao. 2007. Controlling chaotic oscillations via nonlinear observer approach. Chaos, Solitons and Fractals, vol. 34, 1014–1019.
  • Cao YJ. , 2000. A nonlinear adaptive approach to controlling chaotic oscillators. 2000. Phys Lett A; vol. 270, 171–176.
  • Chen G, Dong X. 1993. On feedback control of chaotic continuous-time systems" IEEE Trans Circ Syst, vol. 40, 591–601.
  • Lu J, Zhang S. 2001. Controlling Chen's chaotic attractor using backstepping design based on parameters identification. Phys Lett A, vol. 256, 148–152.
  • Zeng, Y. , Singh, S. N. 1997. Adaptative control of chaos in Lorenz system", Dynamic and Control, vol. 7, 143-154.
  • Kotaro Hirasawa, Xiaofeng Wang, Junichi Murata, Jinglu Hu, Chunzhi Jin, 2000. Universal learning network and its application to chaos control. Neural Networks, Elsevier Science, vol. 13, 239-253
  • SanchezEN, PerezJP, MartinezM, Chen G. 2002. Chaos stabilization: an inverse optimal control approach. Latin Amer Appl Res Int J. , vol. 32, 111–114.
  • Ramirez. J. , B. Castillo-Toledo, J. Gonzalez. 1999. On robust suppression in a class of non driven oscillators: application to the Chua's circuit. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 46, 1150–1152.
  • B. Xian, M. S. Queiroz, D. M. Dawson, and M. L. McIntyre, 2004. A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems. Automatica, vol. 40(4), 695–700.
  • Ge S. , C. Wang, T. H. Lee. 2000. Backstepping control of a class of chaotic systems. International Journal of Bifurcation and Chaos, vol. 10, 1149–1162.
  • Fliess, M. , Levine, J. , Martin, Ph. and Rouchon, P. 1995. Flatness and effect of nonlinear systems: Introductory theory and examples," International Journal of Control, vol 61.
  • Mchiri Mohamed, Belghith Safya, and Khraief Nahla. . Nonlinear Observer Based Control of Uncertain Chaotic Systems. 2011. International Review of Automatic Control (Theory and Applications) - Vol. 4 N. 4, 525-530.