Optimal Control of Nonregular Dynamics in a Duffing Oscillator

Nonlinear Dynamics

Volumn 33, Issue 1, 2003, Pages 71-86

  Lenci, Stefano ^a   Rega, Giuseppe ^b  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Basin erosion; Cross well chaos; Duffing oscillator; Homoclinic bifurcations; One side and global optimal control; Periodic excitation

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; FRACTALS; OPTIMAL CONTROL SYSTEMS;

DUFFING OSCILLATORS;

OSCILLATORS (ELECTRONIC);

EID: 0141958721     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025509014101     Document Type: Article

References (24)

1. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.
2. Moon, F. C., Chaotic and Fractal Dynamics. An Introduction for Applied Scientists and Engineers, Wiley, New York, 1992.
3. Szemplinska-Stupnicka, W. and Rudowski, J., 'Steady state in the twin-well potential oscillator: Computer simulations and approximate analytical studies', Chaos 3, 1993, 375-385.
4. Szemplinska-Stupnicka, W., 'The analytical predictive criteria for chaos and escape in nonlinear oscillators: A survey', Nonlinear Dynamics 7, 1995, 129-147.
5. Thompson, J. M. T. and Stewart, H. B., Nonlinear Dynamics and Chaos, 2nd edition, Wiley, New York, 2002.
6. Wiggins, S., Global Bifurcation and Chaos: Analytical Methods, Springer, New York, 1988.
7. Tseng, W.-Y. and Dugundji, J., 'Nonlinear vibrations of a buckled beam under harmonic excitation', ASME Journal of Applied Mechanics 38, 1971, 467-476.
8. Lenci, S. and Rega, G., 'A procedure for reducing the chaotic response region in an impact mechanical system', Nonlinear Dynamics 15, 1998, 391-409.
9. Lenci, S. and Rega, G., 'Controlling nonlinear dynamics in a two-well impact system. Parts I and II', International Journal of Bifurcation and Chaos 8, 1988, 2387-2424.
10. Lenci, S. and Rega, G., 'A unified control framework of the nonregular dynamics of mechanical oscillators', 2002, submitted.
11. Lenci, S. and Rega, G., 'Optimal control of homoclinic bifurcation: Theoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator', Journal of Vibration and Control 9, 2003, 281-316.
12. Moon, F. C., Johnson, M. A., and Holmes, W. T., 'Controlling chaos in a two-well oscillator', International Journal of Bifurcation and Chaos 6, 1996, 337-347.
13. Hunt, E. R., 'Stabilizing high-periodic orbits in a chaotic system: The diode resonator', Physical Review Letters 67, 1991, 1953-1955.
14. Ott, E., Grebogi, C., and Yorke, J. A., 'Controlling chaos', Physical Review Letters 64, 1990, 1196-1199.
15. Pinto, O. C. and Gonçalves, P. B., 'Non-linear control of buckled beams under step loading', Mechanical Systems and Signal Processing 14, 2000, 967-985.
16. Pinto, O. C. and Gonçalves, P. B., 'Active non-linear control of buckling and vibrations of a flexible buckled beam', Chaos, Solitons and Fractals 14, 2002, 227-239.
17. Osipov, G., Glatz, L., and Troger, H., 'Suppressing chaos in the Duffing oscillator by impulsive actions', Chaos, Solitons and Fractals 9, 1998, 307-321.
18. Agrawal, A. K., Yang, J. N., and Wu, J. C., 'Non-linear control strategies for Duffing systems', International Journal of Non-Linear Mechanics 33, 1998, 829-841.
19. Sifakis, M. K. and Elliott, S. J., 'Strategies for the control of chaos in a Duffmg-Holmes oscillator', Mechanical Systems and Signal Processing 14, 2000, 987-1002.
20. Pyragas, K., 'Continuous control of chaos by self-controlling feedback', Physics Letters A 170, 1992, 421-428.
21. Szemplinska-Stupnicka, W. and Tyrkiel, E., 'Common features of the onset of the persistent chaos in nonlinear oscillators: A phenomenological approach', Nonlinear Dynamics 27, 2002, 217-293.
22. Lansbury, A. N., Thompson, J. M. T., and Stewart, H. B., 'Basin erosion in the twin-well Duffing oscillator: Two distinct bifurcation scenarios', International Journal of Bifurcation and Chaos 2, 1992, 505-532.
23. Thompson, J.M.T., and McRobie, F.A., 'Indeterminate bifurcations and the global dynamics of driven oscillators', in Proceedings of First European Nonlinear Oscillations Conference, Hamburg, August 16-20, E. Kreuzer and G. Schmidt (eds.), Akademie Verlag, Berlin, 1993, pp. 107-128.
24. Lenci, S. and Rega, G., 'Optimal numerical control of single-well to cross-well chaos transition in mechanical systems', Chaos, Solitons and Fractals 15, 2003, 173-186.