On optimal stabilization of periodic orbits via time delayed feedback control

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 8, 1998, Pages 1699-1706

  Basso, M ^a   Genesio, R ^a   Giovanardi, L ^a   Tesi, A ^a   Torrini, G ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040084964     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001376     Document Type: Article

References (16)

1. Abed, E. H. & Wang, H. O. [1995] "Feedback control of bifurcations and chaos in dynamical systems," in Recent Developments in Stochastic and Nonlinear Dynamics: Applications to Mechanical Systems, eds. Namachchivaya, N. S. & Kliemann, W. (CRC Press), pp. 153-173.
2. Basso, M., Genesio, R. & Tesi, A. [1997a] "Stabilizing periodic orbits of forced systems via generalized Pyragas controllers," IEEE Trans. Circuits Syst. I 44, 1023-1027.
3. Basso, M., Genesio, R. & Tesi, A. [1997b] "Stabilization of periodic orbits of forced systems: State of the art and new proposals," Research Report 29/97, Dipartimento di Sistemi e Informatica, Firenze.
4. Chen, G. & Dong, X. [1993] "From chaos to order. Perspective and methodologies in controlling chaotic nonlinear dynamical systems," Int. J. Bifurcation and Chaos 3, 1363-1409.
5. Dressler, U. & Nitsche, G. [1992] "Controlling chaos using time delayed coordinates," Phys. Rev. Lett. 68, 1-4.
6. Hu, G., Qu, Z. & He, K. [1995] "Feedback control of chaos in spatiotemporal systems," Int. J. Bifurcation and Chaos 5, 901-936.
7. Hunt, E. R. [1991] "Stabilizing high-period orbits in chaotic system: The diode resonator," Phys. Rev. Lett. 67, 1953-1955.
8. Just, W., Bernard, T., Ostheirer, M., Reibold, E. & Benner, H. [1997] "Mechanism of the time-delayed feedback control," Phys. Rev. Lett. 78, 203-206.
9. Kittel, A., Parisi, J. & Pyragas, K. [1995] "Delayed feedback control of chaos by self-adapted delay time," Phys. Lett. A198, 433-436.
10. Ogorzalek, M. J. [1993] "Taming chaos - Part II: Control," IEEE Trans. Circuits Syst. 40, 700-706.
11. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
12. Pyragas, K. [1992] "Continuous control of chaos by self-controlling feedback," Phys. Lett. A170, 421-428.
13. Romeiras, F. J., Grebogi, C., Ott, E. & Dayawansa, W. P. [1992] "Controlling chaotic dynamical systems," Physica D58, 165-192.
14. Shinbrot, T., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Using small perturbations to control chaos," Nature 363, 411-417.
15. Socolar, J. E. S., Sukow, D. W. & Gauthier, D. J. [1994] "Stabilizing unstable periodic orbits in fast dynamical systems," Phys. Rev. E50, 3245-3248.
16. Vidyasagar, M. [1992] Nonlinear System Analysis, 2nd edition (Prentice Hall, Englewood Cliffs, NJ).