On time-delayed feedback control of chaotic systems

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

Volumn 46, Issue 6, 1999, Pages 767-772

  Chen, Guanrong ^a   Yu, Xinghuo ^b  

^a UNIVERSITY OF HOUSTON   (United States)

^b CENTRAL QUEENSLAND UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CHAOS THEORY; COMPUTER SIMULATION; FUNCTIONS; LYAPUNOV METHODS; STATE SPACE METHODS; SYSTEM STABILITY;

CHAOS CONTROL; LYAPUNOV FUNCTION; TIME-DELAYED FEEDBACK;

FEEDBACK CONTROL;

EID: 0032642505     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.768837     Document Type: Article

References (18)

1. M.E. Bleich and J. E. S. Socolar, Stability of periodic orbits controlled by time-delayed feedback, Phys. Lett. A, vol. 210, pp. 87-94, 1996.
2. M. E. Bleich and J. E. S. Socolar, Controlling spatiotemporal dynamics with time-delay feedback, Phys. Rev. E. vol. 54, pp. R17-R20, 1996.
3. M. E. Brandt and G. Chen, Controlling the dynamical behavior of a circle map model of the human heart, Biol. Cybern., vol. 74, pp. 1-8, 1996.
4. M. E. Brandt and G. Chen, Feedback control of a quadratic map model of cardiac chaos, Int. J. Bifur. Chaos, vol. 6, pp. 715-723, 1996.
5. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspec-tives, and Applications. Singapore: World Scientific, 1998.
6. G. Chen and X. Dong, On feedback control of chaotic continuous time systems, IEEE Trans. Circuits Syst. I, vol. 40, pp. 591-601, Sept. 1993
7. T. Hikihara, Controlling chaos for magneto-elastic beam by delayed feedback control, in Proc. Int. Conf. Nonlinear Bifurcation Chaos, Lodz-Dobieszkow, Poland, Sept. 16-18, 1996.
8. T. T. Hartley, The extended Poincaré-Bendixson theorem, IEEE Trans. Circuits Syst., vol. 36, pp. 933-934, 1989
9. W. Just, T. Bernard, M. Ostheimer, E. Reibold, and H. Benner, Mech-anism of time-delayed feedback control, Phys. Rev. Lett., vol. 78, pp. 203-206, 1997.
10. H. K. Khalil, Nonlinear Systems, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
11. A. Kittel, J. Parisi, and K. Pyragas, Delayed feedback control of chaos by self-adapted delay time, Phys. Lett. A, vol. 198, pp. 43336, 1995.
12. K. Konishi, M. Ishii, and H. Kokame, Stabilizing unstable periodic points of one-dimensional nonlinear systems using delayed-feedback signals, Phys. Rev. E, vol. 54, pp. 3455-3460, 1996.
13. M. de S. Vieira and A. J. Lichtenberg, Controlling chaos using nonlinear feedback with delay, Phys. Rev. E, vol. 54, pp. 1200-1207, 1996.
14. K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, vol. 170, pp. 42128, 1992.
15. Control of chaos via extended delay feedback, Phys. Lett. A, vol. 206, pp. 323-330, 1995.
16. K. Pyragas and A. Tamasevicius, Experimental control of chaos by delayed self-controlling feedback, Phys. Lett. A, vol. 180, pp. 99-102, 1993.
17. T. Ushio, Limitation of delayed feedback control in nonlinear discretetime systems, IEEE Trans. Circuits Syst. I, vol. 43, pp. 815-816, Sept. 1996.
18. X. Yu, Tracking inherent periodic orbits in chaotic systems via adaptive time delayed self-control, in Proc. IEEE Int. Conf. Decision Control, San Diego, CA, Dec. 10-12, 1997, vol. 1, pp. 40105.