Improvement of time-delayed feedback control by periodic modulation: Analytical theory of Floquet mode control scheme

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 2 2, 2003, Pages 262221-2622210

  Just, Wolfram ^a,b,c   Popovich, Svitlana ^a   Amann, Andreas ^a   Baba, Nilüfer ^a   Schöll, Eckehard ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^c QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; NONLINEAR CONTROL SYSTEMS; PHASE SHIFT;

PERIODIC MODULATIONS;

FEEDBACK CONTROL;

EID: 0038400143     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. R. Bellmann, Introduction to the Mathematical Theory of Control Processes (Academic Press, New York, 1971).
2. H. Nijmeijer and A. Schaft, Nonlinear Dynamical Control Systems (Springer, New York, 1996).
3. K. Ogata, Modern Control Engineering (Prentice-Hall, New York, 1997).
4. E. Ott, C. Grebogi, and Y.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
5. T. Shinbrot, Adv. Phys. 44, 73 (1995).
6. Handbook of Chaos Control, edited by H.G. Schuster (Wiley-VCH, Berlin, 1999).
7. K. Pyragas, Phys. Lett A 170, 421 (1992).
8. S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. E 49, R971 (1994).
9. T. Pierre, G. Bonhomme, and A. Atipo, Phys. Rev. Lett. 76, 2290 (1996).
10. W. Just, T. Bernard, M. Ostheimer, E. Reibold, and H. Benner, Phys. Rev. Lett. 78, 203 (1997).
11. H. Nakajima, Phys. Lett. A 232, 207 (1997).
12. J.E.S. Socolar, D.W. Sukow, and D.J. Gauthier, Phys. Rev. E 50, 3245 (1994).
13. W. Just, D. Reckwerth, E. Reibold, and H. Benner, Phys. Rev. E 59, 2826 (1999).
14. L. Collatz, ZAMM 25/27, 60 (1947).
15. A. Kittel, J. Parisi, and K. Pyragas, Phys. Lett. A 198, 433 (1995).
16. H. Nakajima, H. Ito, and Y. Ueda, IEICE Trans. Fundamentals E80A, 1554 (1997).
17. W. Just, J. Möckel, D. Reckwerth, E. Reibold, and H. Benner, Phys. Rev. Lett. 81, 562 (1998).
18. A.V. Mamaev and M. Saffman, Phys. Rev. Lett. 80, 3499 (1998).
19. R. Bellmann, Differential-Difference Equations (Academic Press, New York, 1963).
20. W. Just, E. Reibold, H. Benner, K. Kacperski, F. Fronczak, and J. Holyst, Phys. Lett. A 254, 158 (1999).
21. W. Just, E. Reibold, K. Kacperski, P. Fronczak, J. Holyst, and H. Benner, Phys. Rev. E 61, 5045 (2000).
22. A. Wacker and E. Schöll, Z. Phys. B: Condens. Matter 93, 431 (1994).
23. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors (Cambridge University Press, Cambridge, 2001).
24. O. Beck, A. Amann, E. Schöll, J.E.S. Socolar, and W. Just, Phys. Rev. E 66, 016213 (2002).
25. G. Franceschini, S. Bose, and E. Schöll, Phys. Rev. E 60, 5426 (1999).
26. N. Baba, A. Amann, E. Schöll, and W. Just, Phys. Rev. Lett. 89, 074101 (2002).
27. H.G. Schuster and M.B. Stemmler, Phys. Rev. E 56, 6410 (1997).
28. W. Just, Physica D 142, 153 (2000).
29. S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993).
30. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations (Springer, New York, 1993).
31. G. Benettin, L. Galgani, A. Giorgilli, and J. Strelcyn, Meccanica 15, 9&21 (1980).
32. M.E. Bleich and J.E.S. Socolar, Phys. Rev. E 54, R17 (1996).