Optimal multi-dimensional OGY controller

Physica D: Nonlinear Phenomena

Volumn 139, Issue 1-2, 2000, Pages 87-96

  Epureanu, Bogdan I ^a   Dowell, Earl H ^a  

^a Duke University   (United States)

Author keywords

Control of chaos; Stabilization of unstable limit cycles

Indexed keywords

EID: 0346480750     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-2789(99)00201-8     Document Type: Article

References (29)

1. G.V. Belyakova, L.A. Belyakov, On bifurcations of periodic orbits in the Van der Pol-Duffing equation, Int. J. Bifurcation Chaos 7 (2) (1997) 459-462.
2. V.N. Belykh, V.V. Bykov, Bifurcations for heteroclinic orbits of a periodic motion and a saddle-focus and dynamical chaos, Solitons and Fractals 9 (1-2) (1998) 1-18.
3. S. Bielawski, D. Derozier, P. Glorieux, Experimental characterization of unstable periodic orbits by controlling chaos, Phys. Rev. A 47 (1993) R2492-R2495.
4. J. Brindley, T. Kapitaniak, M.S. El Naschie, Analytical conditions for strange chaotic and nonchaotic attractors of the quasiperiodically forced Van der Pol equation, Physica D 51 (1) (1989) 28-38.
5. G. Chen, X. Dong, From Chaos to Order - Methodologies, Perspectives, and Applications, 1st ed., World Scientific, Singapore, 1998.
6. M. Ding, W. Yang, V. In, W. Ditto, M.L. Spano, B. Gluckman, Controlling chaos in high dimensions: theory and experiment, Phys. Rev. E 53 (5) (1996) 4334-4344.
7. W.L. Ditto, S.N. Rauseo, M.L. Spano, Experimental control of chaos, Phys. Rev. Lett. 65 (26) (1990) 3211-3214.
8. U. Dressler, G. Nitsche, Controlling chaos using time delay coordinates, Phys. Rev. Lett. 68 (1992) 1-4.
9. B.I. Epureanu, E.H. Dowell, System identification for Ott-Grebogi-Yorke controller design, Phys. Rev. E 56 (5) (1997) 5327-5331.
10. B.I. Epureanu, E.H. Dowell, On the optimality of the OGY control scheme, Physica D 116 (1-2) (1998) 1-7.
11. B.I. Epureanu, S.T. Trickey, E.H. Dowell, Stabilization of unstable limit cycles in systems with limited controllability: Expanding the basin of convergence of OGY-type controllers, Nonlinear Dynamics 15 (2) (1998) 191-205.
12. C.C. Fuh, P.C. Tung, Robust control for a class of nonlinear oscillators with chaotic attractors, Phys. Lett. A 218 (1996) 240-248.
13. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.
14. E.J. Kostelich, C. Grebogi, E. Ott, J.A. Yorke, Higher-dimensional targeting, Phys. Rev. E 47 (1) (1993) 305-310.
15. F.C. Moon, Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, Wiley, New York, 1992.
16. K. Ogata, Control Engineering. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1990.
17. E. Ott, Chaos in Dynamical Systems, Cambridge University Press, New York, 1993.
18. E. Ott, C. Grebogi, J.A. Yorke, Controlling chaos, Phys. Rev. Lett. 64 (11) (1990) 1196-1199.
19. V. Petrov, E. Mihaliuk, S. Scott, K. Showalter, Stabilizing and characterizing unstable states in high-dimensional system from time series, Phys. Rev. E 51 (5) (1995) 3988-3996.
20. G. Quin, D. Dong, R. L, X. Wen, Rich bifurcation behaviors of the driven Van der Pol oscillator, Phys. Lett. A 141 (1) (1989) 412-416.
21. F.J. Romeiras, C. Grebogi, E. Ott, W.P. Dayawansa, Controlling chaotic dynamical systems, Physica D 58 (1992) 165-192.
22. S.H. Strogatz, Nonlinear Dynamics and Chaos, Addison-Wesley, Reading, MA, 1994.
23. W. Szemplinska Stupnicka, J. Rudowski, The coexistence of periodic, almost-periodic and chaotic attractors in the Van der Pol-Duffing oscillator, Journal of Sound and Vibration 199 (2) (1997) 165-175.
24. Z. Toroczkai, Geometric method for stabilizing unstable periodic orbits, Phys. Lett. A 190 (1994) 71-78.
25. A. Venkatesan, M. Lakshmanan, Bifurcation and chaos in the double-well Duffing-Van der Pol oscillator: numerical and analytical studies, Phys. Rev. E 56 (6) (1997) 6321-6330.
26. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, 1990.
27. D. Xu, S.R. Bishop, Self-locating control of chaotic systems using newton algorithm, Phys. Rev. A 210 (1996) 273-278.
28. J.X. Xu, J. Jiang, The global bifurcation characteristics of the forced Van der Pol oscillator, Solitons and Fractals 7 (1) (1996) 3-19.
29. P. Yu, K. Huseyin, Parametrically excited non-linear systems: a comparison of certain methods, Int. J. Non-linear Mech. 33 (6) (1998) 967-978.