State space reconstruction using extended state observers to control chaos in a nonlinear pendulum

International Journal of Bifurcation and Chaos

Volumn 15, Issue 12, 2005, Pages 4051-4063

  Pereira Pinto, Francisco Heitor I ^a   Ferreira, Armando M ^a   Savi, Marcelo A ^b  

^a MILITARY INSTITUTE OF ENGINEERING   (Brazil)

^b FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Chaos; Control; Nonlinear pendulum; State space reconstruction; Time series

Indexed keywords

NONLINEAR SYSTEMS; PENDULUMS; PERTURBATION TECHNIQUES; TIME SERIES ANALYSIS;

NONLINEAR PENDULUM; PERIODIC ORBITS; STATE SPACE RECONSTRUCTION;

CHAOS THEORY;

EID: 20844441860     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405014490     Document Type: Article

References (28)

1. Auerbach, D., Cvitlanovic, P., Eckmann, J.-P., Gunaratne, G. & Procaccia, I. [1987] "Exploring chaotic motion through periodic orbits," Phys. Rev. Lett. 58, 2387-2389.
2. Bowong, S. & Kakmeni, F. M. M. [2003] "Chaos control and duration time of a class of uncertain chaotic systems," Phys. Lett. A316, 206-217.
3. Broomhead, D. S. & King, G. P. [1986] "Extracting qualitative dynamics from experimental data," Physica D20, 217-236.
4. Cao, Y. J. [2000] "A nonlinear adaptative approach to controlling chaotic oscillators," Phys. Lett. A270, 171-176.
5. Dressler, U. & Nitsche, G. [1992] "Controlling chaos using time delay coordinates," Phys. Rev. Lett. 68, 1-4.
6. Femat, R., Ramírez, J.-A. & González, J. [1997] "A strategy to control chaos in nonlinear driven oscillators with least prior knowledge," Phys. Lett. A224, 271-276.
7. Franca, L. F. P. & Savi, M. A. [2001] "Distinguishing periodic and chaotic time series obtained from an experimental nonlinear pendulum," Nonlin. Dyn. 26, 253-271.
8. Gao, Z., Huang, Y. & Han, J. [2001] "An alternative paradigm for control system design," IEEE Conf. Decision and Control.
9. Gao, Z. [2003] "Scaling and bandwidth-parameterization based controller tuning," in American Control Conf., Denver, Colorado.
10. Gunaratne, G., Linsay, P. S. & Vinson, M. J. [1989] "Chaos beyond onset: A. comparison of theory and experiment," Phys. Rev. Lett. 63, 1-4.
11. Han, J. [1995] "A class of extended state observers for uncertain systems," Contr. Decis. 10, 85-88.
12. Hübinger, B., Doerner, R., Martienssen, W., Herdering, M., Pitka, R. & Dressler, U. [1994] "Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents," Phys. Rev. E50, 932-948.
13. Kalman, R. E. [1960] "A new approach to linear filtering and prediction problems," Trans. ASME - J. Basic Engin. D82, 35-45.
14. Korte, R. J. de, Schouten, J. C. & van den Bleek, C. M. V. [1995] "Experimental control of a chaotic pendulum with unknown dynamics using delay coordinates," Phys. Rev. E52, 3358-3365.
15. Luenberger, D. G. [1964] "Observing the state of a linear system," IEEE Trans. Milit. Electron. v.MIL 8.
16. Luenberger, D. G. [1966] "Observers for multivariable systems," IEEE Trans. Autom. Contr. AC 11.
17. Otani, M. & Jones, A. J. [1997] "Guiding chaotic orbits," 1.30, Research Report - Imperial College of Science Technology and Medicine, London.
18. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
19. Packard, N. J., Crutchfield, J. P., Fromer, J. D. & Shaw, R. S. [1980] "Geometry from a time-series," Phys. Rev. Lett. 45, 712-716.
20. Pereira-Pinto, F. H. I., Ferreira, A. M. & Savi, M. A. [2004] "Chaos control in a nonlinear pendulum using a semi-continuous method," Chaos Solit. Fract. 22, 653-668.
21. Pinto, E. G. F. & Savi, M. A. [2003] "Nonlinear prediction of time series obtained from an experimental pendulum," Current Topics in Acoustical Research - Research Trends, Vol. 3, pp. 151-162.
22. Pyragas, K. [1992] "Continuous control of chaos by self-controlling feedback," Phys. Lett. A170, 421-428.
23. Ramirez, J.-A. & Villamil, F.-V. [1995] "State estimation for a class of nonlinear oscillators with chaotic attractor," Phys. Lett. A197, 116-120.
24. Ruelle, D. [1979] "Ergodic theory of differentiable dynamical systems," Mathématique, of the Institut des Hautes Études Scientifiques, Vol. 5, pp. 27.
25. So, P., Ott, E. & Dayawansa, W. P. [1994] "Observing chaos: Deducing and tracking the state of a chaotic system from limited observation," Phys. Rev. E49, 2650-2660.
26. Takens, F. [1981] "Detecting strange attractors in turbulence," in Proc. Symp. Dynamical Systems and Turbulence, University of Warwick, 1979-1980, eds. Rand, D. A. & Young, L. S. (Springer, Berlin).
27. Wang, W. & Gao, Z. |2003] "A. comparison study of advanced state observer design techniques," in American Control Conf., Denver, Colorado, June.
28. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D16, 285-317.