Controlling chaos in high dimensions

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 44, Issue 10, 1997, Pages 971-975

  Grebogi, Celso ^a   Lai, Ying Cheng ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Chaos; Control; Pole placement technique

Indexed keywords

CHAOS THEORY; FEEDBACK CONTROL; TIME SERIES ANALYSIS;

OTT GREBOGI YORKE (OGY) METHOD; POLE PLACEMENT TECHNIQUE;

TIME VARYING CONTROL SYSTEMS;

EID: 0031258181     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.633886     Document Type: Article

References (23)

1. E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos," Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.
2. "Controlling chaotic dynamical systems," pp. 153-172 in CHAOS/XAOC, Soviet-Amer. Perspective on Nonlinear Science, D. Campbell, Ed. New York: Amer. Inst. Phys., 1990.
3. S. Hayes, C. Grebogi, and E. Ott, "Communicating with chaos," Phys. Rev. Lett., vol. 70, pp. 3031-3034, 1993.
4. C. Grebogi, E. Ott, and J. A. Yorke, "Unstable periodic orbits and the dimension of chaotic attractors," Phys. Rev. A, vol. 37, pp. 1711-1724, 1988.
5. F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, "Controlling chaotic dynamical systems," Physica D, vol. 58, pp. 165-192, 1992.
6. C. Grebogi, E. Kostelich, E. Ott, and J. A. Yorke, "Multidimensional intertwined basin boundaries: basin structure of the kicked double rotor," Physica D, vol. 25, pp. 347-360, 1987.
7. K. Ogata, Modern Control Engineering, 2nd Ed. Englewood Cliffs, NJ: Prentice-Hall, 1990.
8. J. M. T. Thompson and S. R. Bishop, Nonlinearity and Chaos in Engineering Dynamics. New York: Wiley, 1994.
9. C. Grebogi, E. Ott, and J. A. Yorke, "Crises, sudden changes in chaotic attractors and chaotic transients," Physica D, vol. 7, pp. 181-200, 1983.
10. C. Grebogi, E. Ott, F. J. Romeiras, and J. A. Yorke, "Critical exponents for crisis-induced intermittency," Phys. Rev. A, vol. 36, pp. 5365-5380, 1987.
11. F. Takens, "Detecting strange attractors in turbulence," pp. 366-381 in Dynamical Systems and Turbulence (Lecture Notes in Mathematics, vol. 898). D. A. Rand and L.-S. Young, Eds. New York: Springer, 1980.
12. T. Sauer, J. A. Yorke, and M. Casdagli, "Embedology," J. Stat. Phys., vol. 65, pp. 579-616, 1991.
13. U. Dressier and G. Nitsche, "Controlling chaos using time delay coordinates," Phys. Rev. Lett., vol. 68, pp. 1-4, 1992.
14. W. L. Ditto, S. N. Rauseo, and M. L. Spano, "Experimental control of chaos," Phys. Rev. Lett., vol. 65, pp. 3211-3214, 1990.
15. T. Shinbrot, E. Ott, C. Grebogi, and J. A. Yorke, "Using chaos to direct trajectories to targets," Phys. Rev. Lett., vol. 65, pp. 3215-3218, 1990.
16. E. J. Kostelich, C. Grebogi, E. Ott, and J. A. Yorke, "High dimensional targeting," Phys. Rev. E, vol. 47, pp. 305-310, 1993.
17. E. Barreto and C. Grebogi, "Multiparameter control of chaos," Phys. Rev. E, vol. 52, pp. 3553-3557, 1995.
18. Y.-C. Lai and C. Grebogi, "Synchronization of chaotic trajectories using control," Phys. Rev. E, vol. 47, pp. 2357-2360, 1993.
19. "Converting transient chaos into sustained chaos by feedback control," Phys. Rev. E, vol. 49, pp. 1094-1099, 1994.
20. Y. Nagai and Y.-C. Lai, "Selection of desirable chaotic phase using small feedback control," Phys. Rev. E, vol. 51, pp. 3842-3848, 1995.
21. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "Phase synchronization of chaotic oscillators," Phys. Rev. Lett., vol. 76, pp. 1804-1807, 1996.
22. S. Hayes, C. Grebogi, E. Ott, and A. Mark, "Experimental control of chaos for communication," Phys. Rev. Lett., vol. 73, pp. 1781-1784, 1994.
23. E. Rosa, S. Hayes, and C. Grebogi, "Noise filtering in communicating with chaos," Phys. Rev. Lett., vol. 78, pp. 1247-1250, 1997.