Stabilization of unstable fixed points with queue-based delayed feedback control

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 18, Issue 5, 2011, Pages 679-693

  Konishi, Keiji ^a   Hara, Naoyuki ^b  

^a Osaka Prefecture University   (Japan)

^b NONE

Author keywords

Controlling chaos; Delayed feedback control; FIFO queue; Semi discretization; Unstable fixed point

Indexed keywords

EID: 80054065542     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (43)

1. K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos, Springer, 1996.
2. S. Bielawski, D. Derozier, and P. Glorieux, Experimental characterization of unstable periodic orbits by controlling chaos, Phys. Rev. A, 47, (1992) 2492-2495.
3. T. L. Carroll, I. Triandaf, I. Schwartz, and L. Pecora, Tracking unstable orbits in an experiment, Phys. Rev. A, 46, (1992) 6189-6192.
4. P. Celka, Experimental verification of Pyragas's chaos control method applied to Chua's circuit, Int. J. of Bifurcations and Chaos, 4, (1994) 1703-1706.
5. A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, Stabilizing unstable steady states using extended time-delay autosynchronization, Chaos, 8, (1998) 782-790. (Pubitemid 128449107)
6. G. Chen, Chaos: its control and generation for engineering applications, Dyn. Con. Dis. and Impl. Sys. B, 10, (2003) 235-245. (Pubitemid 39266230)
7. T. Dahms, P. Hövel, and E. Schöll, Control of unstable steady states by extended time-delayed feedback, Phys. Rev. E, 76, (2007) 056201.
8. B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll, Refuting the odd number limitation of time-delayed feedback control, Phys. Rev. Lett., 98, (2007) 114101.
9. G. Franklin, J. Powell, and M. Workman, Digital Control of Dynamic Systems (Third Edition), Prentice Hall, 1997.
10. Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Tracking unstable steady states: Extending the stability regime of a multimode laser system, Phys. Rev. Lett., 69, (1992) 3169-3172.
11. A. Gjurchinovski and V. Urumov, Stabilization of unstable steady states by variabledelay feedback control, Europhys. Lett., 84, (2008) 40013.
12. A. Gjurchinovski and V. Urumov, Variable-delay feedback control of unstable steady states in retarded time-delayed systems, Phys. Rev. E, 81, (2010) 016209.
13. K. Gu and S. Niculescu, Survey on recent results in the stability and control of time-delay systems, J. Dyn. Sys., Meas., Control, 125, (2003) 158-165.
14. F. Hartung, T. Insperger, G. Stepan, and J. Turi, Approximate stability charts for milling processes using semi-discretization, Appl. Math. Comput., 174, (2006) 51-73. (Pubitemid 43288937)
15. K. Hirata, H. Kokame, K. Konishi, and H. Fujita, Observer-based delayed-feedback control of continuous-time systems, Proc. of American Control Conference, (2001) 25-27.
16. P. Hövel and E. Schöll, Control of unstable steady states by time-delayed feedback methods, Phys. Rev. E, 72, (2005) 046203.
17. T. Imai, K. Konishi, H. Kokame, and K. Hirata, An experimental suppression of spatial instability in one-way open coupled Chua's circuits, Int. J. of Bifurcations and Chaos, 12, (2002) 2897-2905. (Pubitemid 36261592)
18. T. Insperger and G. Stepan, Semi-discretization method for delayed systems, Int. J. Numer. Meth. Engng, 55, (2002) 503-518.
19. T. Insperger, G. Stepan, and J. Turi, On the higher-order semi-discretizations for periodic delayed systems, Journal of Sound and Vibration, 313, (2008) 334-341.
20. T. Insperger, G. Stepan, and J. Turi, Delayed feedback of sampled higher derivatives, Phil. Trans. R Soc. A, 368, (2010) 469-482.
21. W. Just, On the eigenvalue spectrum for time-delayed Floquet problems, Physica D, 142, (2000) 153-165.
22. A. Kittel, J. Parisi, K. Pyragas, and R. Richter, Delayed feedback control of chaos in an electronic double-scroll oscillator. Z. Naturforsch, 49 a, (1994) 843-846.
23. H. Kokame, K. Hirata, K. Konishi, and T. Mori, State difference feedback for stabilizing uncertain steady states of non-linear systems. Int. J. Control, 74, (2001) 537-546.
24. K. Konishi and H. Kokame, Stabilizing and tracking unstable focus points in chaotic systems using a neural network, Phys. Lett. A, 206, (1995) 203-210.
25. K. Konishi, K. Senda, and H. Kokame, Amplitude death in time-delay chaotic oscillators coupled by diffusive connections, Phys. Rev. E, 78, (2008) 056216.
26. K. Konishi, H. Kokame, and N. Hara, Stabilization of a steady state in network oscillators by using diffusive connections with two long time delays, Phys. Rev. E, 81, (2010) 016201.
27. K. Konishi and N. Hara, Delayed feedback control based on the act-and-wait concept, Nonlinear Dyn. 63, (2011) 513-519.
28. B. MacKe, J. Zemmouri, and N. E. Fettouhi, Stabilization of unstable stationary states in optical bistability, Phys. Rev. A, 47, (1993) 1609-1611.
29. W. Michiels, V. V. Assche, and S.-I. Niculescu, Stabilization of time-delay systems with a controlled time-varying delay and applications, IEEE Trans. Automatic Control, 50, (2005) 493-504. (Pubitemid 40555771)
30. H. Nakajima, On analytical properties of delayed feedback control of chaos, Phys. Lett. A, 232, (1997) 207-210. (Pubitemid 127378607)
31. K. Ogata, Discrete-time control systems, Pearson Education, 1994.
32. C. M. Postlethwaite and M. Silber, Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control, Phys. Rev. E, 76, (2007) 056214.
33. K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170, (1992) 421-428.
34. K. Pyragas, Delayed feedback control of chaos, Phil. Trans. R Soc. A, 364, (2006) 2309-2334. (Pubitemid 44328172)
35. K. Pyragas, V. Pyragas, I. Kiss, and J. Hudson, Adaptive control of unknown unstable steady states of dynamical systems, Phys. Rev. E, 70, (2004) 026215.
36. D. Reddy, A. Sen, and G. Johnston, Experimental evidence of time-delay induced death in coupled limit-cycle oscillators, Phys. Rev. Lett., 85, (2000) 3381-3384.
37. E. Scholl and H. Schuster, Handbook of chaos control, Wiley-Vch, 2008.
38. I. B. Schwartz and I. Triandaf, Tracking unstable orbits in experiments, Phys. Rev. A, 46, (1992) 7439-7444.
39. J. Sieber, A. Gonzalez-Buelga, S. A. Neild, D. J. Wagg, and B. Krauskopf, Experimental continuation of periodic orbits through a fold, Phys. Rev. Lett., 100, (2008) 244101.
40. J. Sieber, B. Krauskopf, D. J. Wagg, S. A. Neild, and A. Gonzalez-Buelga, Controlbased continuation of unstable periodic orbits, J. Comput. Nonlinear Dynam., 6, (2011) 011005.
41. V. Tronciu, H.-J. Wünsche, M. Wolfrum, and M. Radziunas, Semiconductor laser under resonant feedback from a Fabry-Perot resonator: stability of continuous-wave operation, Phys. Rev. E, 73, (2006) 046205.
42. H. Voss, Real-time anticipation of chaotic states of an electronic circuit, Int. J. of Bifurcations and Chaos, 12, (2002) 1619-1625.
43. S. Yanchuk, M. Wolfrum, P. Hövel, and E. Schöll, Control of unstable steady states by long delay feedback, Phys. Rev. E, 74, (2006) 026201. Received July 2010; revised March 2011.