Designing hopf bifurcations into nonlinear discrete-time systems via feedback control

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 14, Issue 7, 2004, Pages 2283-2293

  Wen, Guilin ^a   Xu, Daolin ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Bifurcation control; Discrete time system; Hopf bifurcation; Washout filters

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; FEEDBACK CONTROL; NONLINEAR CONTROL SYSTEMS; OSCILLATORS (MECHANICAL); PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; RESONANCE; WAVE FILTERS;

BIFURCATION CONTROL; DISCRETE-TIME SYSTEMS; HOPF BIFURCATION; WASHOUT FILTERS;

BIFURCATION (MATHEMATICS);

EID: 13844275807     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404010679     Document Type: Article

References (25)

1. Abed, E. H. & Fu, J. H. [1986] "Local feedback stabilization and bifurcation control, 1: Hopf bifurcation," Syst. Contr. Lett. 7, 11-17.
2. Abed, E. H. [1995] "Bifurcation-theoretic issues in the control of voltage collapse," in Proc. IMA Workshop on Systems and Control Theory for Power Systems, eds. Chow, J. H., Kokotovic, P. V. & Thomas, R. J. (Springer-Verlag, NY), pp. 1-21.
3. Alonso, D., Paolini, E. & Moiola, J. L. [2001] "An experimental application of the anticontrol of Hopf bifurations," Int. J. Bifurcation and Chaos 11, 1977-1987.
4. Aronson, D. G., Chory, M. A., Hall, G. R. & McGehee, R. P. [1982] "Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer assisted study," Commun. Math. Phys. 83, 303-354.
5. Berns, D. W., Moiola, J. L. & Chen, G. [1998] "Feedback control of limit circle amplitudes from a frequency domain approach," Automatica 34, 1567-1573.
6. Carr, J. [1981] Applications of Center Manifold Theory, Applied Mathematical Sciences, Vol. 35 (Springer-Verlag), pp. 33-36.
7. Chen, G., Wang, H. O., Howle, L. E., Gustafson, M. R. & Meressi, T. [1998] "Amplitude control of bifurcation and application to Rayleigh-Benard convection," in Proc. 37th IEEE Conf. Decision and Control, pp. 1951-1956.
8. Chen, D., Wang, H. O. & Chen, G. [2001] "Anti-control of Hopf bifurcation," IEEE Trans. Circuits Syst.-I 48, 661-672.
9. Chenciner, A. [1985a] "Bifurcations De points fixes elliptiques I.-Courbes invariantes," Publ. Math. IHES 61, 67-127.
10. Chenciner, A. [1985b] "Bifurcation de points fixes elliptiques II.-Orbites oeriodiques et ensembles de Cantor invariants," Invent. Math. 80, 81-106.
11. Frouzakis, C. E., Adomaitis, R. A. & Kevrekidis, I. G. [1991] "Resonance phenomena in an adaptively-controlled system," Int. J. Bifurcation and Chaos 1, 83-106.
12. Golubitsky, M. & Schaeffter, D. G. [1985] Singularities and Groups in Bifurcation Theory (Springer-Verlag, NY).
13. Hill, D. L. [2001] "On the control of high dimensional chaotic dynamical systems using nonlinear approximations," Int. J. Bifurcation and Chaos 11, 1753-1760.
14. Iooss, G. [1979] Bifurcation of Maps and Applications, Math. Studies, Vol. 36 (North-Holland, Amsterdam).
15. Lasalle, J. P. [1986] The Stability and Control of Discrete Processes (Springer-Verlag).
16. Lee, H. C. & Abed, E. H. [1991] "Wahout filters in the bifurcation control of high alpha flight dynamics," in Proc. American Control Conf. (Boston), pp. 206-211.
17. Moiola, J. L., Berns, D. W. & Chen, G. [1999] "Controlling degenerate Hopf bifurcations," Lat. Amer. Appl. Res. 29, 213-220.
18. Moiola, J. L. & Chua, L. O. [1999] "Hopf bifurcations and degeneracy in Chua's circuit - a perspective from a frequency domain approach," Int. J. Bifurcation and Chaos 9, 295-303.
19. Wan, Y. H. [1978] "Bifurcation into invariant tori at points of resonance," Arch. Rat. Mech. Anal. 68, 343-357.
20. Wang, H. O., Abed, E. H. & Hamdan, A. M. A. [1994] "Bifurcations, chaos and crises in voltage collapse of a model power system," IEEE Trans. Circuits Syst.-I 41, 294-302.
21. Wang, H. O. & Abed, E. H. [1995] "Bifurcation control of a chaotic system," Automatica 31, 1213-1226.
22. Wang, H. O., Chen, D. & Chen, G. [1998] "Bifurcation control of pathological heart rhythms," in Proc. IEEE Conf. Control Applications, Triese, Italy, Sept. 1-4, 1998, pp. 858-862.
23. Wen, G. L., Xu, D. & Han, X. [2002] "On creation of Hopf bifurcations in discrete-time nonlinear systems," Chaos 12, 350-355.
24. Wen, G. L. & Xu, D. [2004] "Implicit criteria of eigen-value assignment and transversility for bifurcation control in four-dimensional maps," Int. Bifurcation and Chaos 14, to appear.
25. Yuen, P. K. & Bau, H. H. [1996] "Rendering a subcritical Hopf bifurcation supercritical," J. Fluid Mech. 317, 91-109.