Design and experimental verification of multiple delay feedback control for time-delay nonlinear oscillators

Nonlinear Dynamics

Volumn 67, Issue 2, 2012, Pages 1407-1418

  Le, Luan Ba ^a   Konishi, Keiji ^a   Hara, Naoyuki ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

Chaos; Delayed feedback control; Electronic circuits; Time delay nonlinear oscillators

Indexed keywords

ANALYTICAL RESULTS; BOUNDARY CURVES; CONTROL PARAMETERS; DELAY TIME; DELAYED FEEDBACK CONTROL; EXPERIMENTAL VERIFICATION; FEEDBACK GAIN; MULTIPLE DELAY FEEDBACK CONTROLS; NON-LINEAR OSCILLATORS; UNSTABLE FIXED POINT;

CHAOS THEORY; CONTROL SYSTEM ANALYSIS; CONTROLLERS; DELAY CIRCUITS; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR STABILITY ANALYSIS; NETWORKS (CIRCUITS); OSCILLATORS (MECHANICAL); TIME DELAY;

NONLINEAR FEEDBACK;

EID: 84855778993     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0077-4     Document Type: Article

References (58)

1. Chen, G.; Dong, X.: From Chaos to Order. World Scientific, Singapore (1998)
2. Schuster, H.G.: Handbook of Chaos Control. Wiley, New York (1999)
3. B.R. Andrievskii A.L. Fradkov 2003 Control of chaos: Methods and applications-I. Methods Autom. Remote Control 64 673 713 1107.37302 2093398 10.1023/A:1023684619933 (Pubitemid 36572420)
4. B.R. Andrievskii A.L. Fradkov 2004 Control of chaos: Methods and applications-II. Applications Autom. Remote Control 65 505 533 1115.37315 2095138 10.1023/B:AURC.0000023528.59389.09 (Pubitemid 39018535)
5. Schöll, E.; Schuster, H.G.: Handbook of Chaos Control. Wiley, New York (2008)
6. K. Pyragas 1992 Continuous control of chaos by self-controlling feedback Phys. Lett. A 170 421 428 10.1016/0375-9601(92)90745-8
7. K. Pyragas 2006 Delayed feedback control of chaos Philos. Trans. R. Soc. Lond. A 364 2309 2334 1152.93477 2251252 10.1098/rsta.2006.1827 (Pubitemid 44328172)
8. K. Gu S.I. Niculescu 2003 Survey on recent results in the stability and control of time-delay systems J. Dyn. Syst. Meas. Control 125 158 165 10.1115/1.1569950
9. A. Chang J.C. Bienfang G.M. Hall J.R. Gardner D.J. Gauthier 1998 Stabilizing unstable steady states using extended time-delay autosynchronization Chaos 8 782 790 1003.37509 10.1063/1.166357 (Pubitemid 128449107)
10. P. Hövel E. Schöll 2005 Control of unstable steady states by time-delayed feedback methods Phys. Rev. E 72 046203 10.1103/PhysRevE.72.046203 (Pubitemid 41777957)
11. T. Dahms P. Hövel E. Schöll 2007 Control of unstable steady states by extended time-delayed feedback Phys. Rev. E 76 056201 2495367 10.1103/PhysRevE.76.056201
12. H. Kokame K. Hirata K. Konishi T. Mori 2001 State difference feedback for stabilizing uncertain steady states of non-linear systems Int. J. Control 74 537 546 1038.93078 1827540 10.1080/00207170010017275
13. H. Kokame K. Hirata K. Konishi T. Mori 2001 Difference feedback can stabilize uncertain steady states IEEE Trans. Autom. Control 46 1908 1913 1032.93065 1878211 10.1109/9.975474 (Pubitemid 34126236)
14. Hirata, K.; Kokame, H.; Konishi, K.; Fujita, H.: Observer-based delayed-feedback control of continuous-time systems. In: Proc. of American Control Conference, pp. 25-27 (2001)
15. V.Z. Tronciu H.-J. Wünsche M. Wolfrum M. Radziunas 2006 Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation Phys. Rev. E 73 046205 10.1103/PhysRevE.73.046205
16. A. Ahlborn U. Parlitz 2004 Stabilizing unstable steady states using multiple delay feedback control Phys. Rev. Lett. 93 264101 10.1103/PhysRevLett. 93.264101 (Pubitemid 40213727)
17. A. Ahlborn U. Parlitz 2005 Controlling dynamical systems using multiple delay feedback control Phys. Rev. E 72 016206 2178377 10.1103/PhysRevE.72.016206 (Pubitemid 41521121)
18. A. Ahlborn U. Parlitz 2006 Laser stabilization with multiple-delay feedback control Opt. Lett. 31 465 467 10.1364/OL.31.000465
19. T. Hikihara T. Kawagoshi 1996 An experimental study on stabilization of unstable periodic motion in magneto-elastic chaos Phys. Lett. A 211 29 36 10.1016/0375-9601(95)00925-6 (Pubitemid 126367606)
20. A. Kittel J. Parisi K. Pyragas R. Richter 1994 Delayed feedback control of chaos in an electronic double-scroll oscillator Z. Naturforsch. 49a 843 846
21. Konishi, K.; Kokame, H.: Odd-number property of multiple delayed feedback control. In: Proc. of the 15th International IEEE Workshop on Nonlinear Dynamics of Electronic Systems, pp. 249-252 (2007)
22. J. Lu Z. Ma L. Li 2009 Double delayed feedback control for the stabilization of unstable steady states in chaotic systems Commun. Nonlinear Sci. Numer. Simul. 14 3037 3045 1221.37217 2502313 10.1016/j.cnsns.2008.10.026
23. J.D. Farmer 1982 Chaotic attractors of an infinite-dimensional dynamical system Physica D 4 366 393 1194.37052 657740 10.1016/0167-2789(82)90042-2
24. MacDonald, N.: Biological Delay Systems: Linear Stability Theory. Cambridge University Press, Cambridge (1989)
25. H.U. Voss 2000 Anticipating chaotic synchronization Phys. Rev. E 61 5115 5119 10.1103/PhysRevE.61.5115
26. M. Bunner W. Just 1998 Synchronization of time-delay systems Phys. Rev. E 58 4072 4075 10.1103/PhysRevE.58.R4072
27. E.M. Shahverdiev K.A. Shore 2005 Generalized synchronization in time-delayed systems Phys. Rev. E 71 016201 10.1103/PhysRevE.71.016201 (Pubitemid 40629775)
28. S. Sano A. Uchida S. Yoshimori R. Roy 2007 Dual synchronization of chaos in Mackey-Glass electronic circuits with time-delayed feedback Phys. Rev. E 75 016207 10.1103/PhysRevE.75.016207 (Pubitemid 46134141)
29. W.H. Kye M. Choi C.M. Kim 2005 Encryption with synchronized time-delayed systems Phys. Rev. E 71 045202 2139984 10.1103/PhysRevE.71.045202 (Pubitemid 40629683)
30. M. Suzuki N. Sakamoto 2010 Controlling ideal turbulence in time-delayed Chua's circuit: Stabilization and synchronization Int. J. Bifurc. Chaos Appl. Sci. Eng. 20 1351 1363 1193.35231 2669541 10.1142/S0218127410026526
31. C.F. Feng 2010 Projective synchronization between two different time-delayed chaotic systems using active control approach Nonlinear Dyn. 62 453 459 1211.93064 10.1007/s11071-010-9733-3
32. Moon, F.C.: Dynamics and Manufacturing Processes. Wiley, New York (1998)
33. Radons, G.; Neugebauer, R.: Nonlinear Dynamics of Production Systems. Wiley, New York (2004)
34. N. Sowa T. Kondou H. Mori M.S. Choi 2006 Method of preventing unstable vibration caused by time delays in contact rotating systems: Application of new stability analysis JSME Int. J. Ser. C, Dyn. Control Robot. Des. Manuf. 49 973 982 10.1299/jsmec.49.973 (Pubitemid 47288071)
35. A. Namajunas K. Pyragas A. Tamaševičius 1995 Stabilization of an unstable steady state in a Mackey-Glass system Phys. Lett. A 204 255 262 10.1016/0375-9601(95)00480-Q
36. X. Guan G. Feng C. Chen G. Chen 2007 A full delayed feedback controller design method for time-delay chaotic systems Physica D 227 36 42 1158.34343 2305197 10.1016/j.physd.2006.12.009
37. A. Gjurchinovski V. Urumov 2010 Variable-delay feedback control of unstable steady states in retarded time-delayed systems Phys. Rev. E 81 016209 10.1103/PhysRevE.81.016209
38. Hale, J.K.; Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
39. Michiels, W.; Niculescu, S.I.: Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach. SIAM, Philadelphia (2007)
40. M. Ishii K. Konishi H. Kokame 1997 Robust stability of extended delayed-feedback control in one-dimensional chaotic systems Phys. Lett. A 235 603 609 10.1016/S0375-9601(97)00687-7 (Pubitemid 127379664)
41. K. Konishi K. Senda H. Kokame 2008 Amplitude death in time-delay chaotic oscillators coupled by diffusive connections Phys. Rev. E 78 056216 2551384 10.1103/PhysRevE.78.056216
42. K.B. Blyuss Y.N. Kyrychko P. Hövel E. Schöll 2008 Control of unstable steady states in neutral time-delayed systems Eur. Phys. J. B 65 571 576 1188.93033 10.1140/epjb/e2008-00371-x
43. S. Xu J. Lam Y. Zou 2005 Delay-dependent approach to stabilization of time-delay chaotic systems via standard and delayed feedback controllers Int. J. Bifurc. Chaos Appl. Sci. Eng. 15 1455 1465 1089.93017 2152085 10.1142/S0218127405012570 (Pubitemid 40970591)
44. B. Rezaie M.R.J. Motlagh M. Analoui S. Khorsandi 2009 Stabilizing fixed points of time-delay systems close to the Hopf bifurcation using a dynamic delayed feedback control method J. Phys. A, Math. Theor. 42 395102 10.1088/1751-8113/42/39/395102
45. N. Vasegh A.K. Sedigh 2008 Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation Phys. Lett. A 372 5110 5114 1221.34164 10.1016/j.physleta.2008.06.023
46. N. Vasegh A.K. Sedigh 2009 Chaos control via TDFC in time-delayed systems: The harmonic balance approach Phys. Lett. A 373 354 358 05983196 10.1016/j.physleta.2008.11.050
47. K. Konishi H. Kokame N. Hara 2010 Stabilization of a steady state in network oscillators by using diffusive connections with two long time delays Phys. Rev. E 81 016201 10.1103/PhysRevE.81.016201
48. T. Ushio 1996 Limitation of delayed feedback control in nonlinear discrete-time systems IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 43 815 816 10.1109/81.536757 (Pubitemid 126777531)
49. H. Nakajima 1997 On analytical properties of delayed feedback control of chaos Phys. Lett. A 232 207 210 1053.93509 1469909 10.1016/S0375-9601(97)00362-9 (Pubitemid 127378607)
50. W. Just E. Reibold H. Bennerb K. Kacperskic P. Fronczakc J. Holyst 1999 Limits of time-delayed feedback control Phys. Lett. A 254 158 164 10.1016/S0375-9601(99)00113-9
51. B. Fiedler V. Flunkert M. Georgi P. Hövel E. Schöll 2007 Refuting the odd number limitation of time-delayed feedback control Phys. Rev. Lett. 98 114101 10.1103/PhysRevLett.98.114101 (Pubitemid 46434099)
52. W. Just B. Fiedler M. Georgi V. Flunkert P. Hövel E. Schöll 2007 Beyond the odd number limitation: A bifurcation analysis of time-delayed feedback control Phys. Rev. E 76 026210 2365548 10.1103/PhysRevE.76.026210 (Pubitemid 47267866)
53. C.M. Postlethwaite M. Silber 2007 Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control Phys. Rev. E 76 056214 2495373 10.1103/PhysRevE.76.056214 (Pubitemid 350205868)
54. K. Konishi H. Kokame 1998 Observer-based delayed-feedback control for time-discrete chaotic systems Phys. Lett. A 248 359 368 10.1016/S0375-9601(98) 00673-2 (Pubitemid 128400032)
55. S. Yamamoto T. Hino T. Ushio 2001 Dynamic delayed feedback controllers for chaotic discrete-time systems IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48 785 789 1159.93329 10.1109/81.928162 (Pubitemid 32609783)
56. K. Pyragas V. Pyragas I.Z. Kiss J.L. Hudson 2002 Stabilizing and tracking unknown steady states of dynamical systems Phys. Rev. Lett. 89 244103 10.1103/PhysRevLett.89.244103
57. K. Pyragas V. Pyragas I.Z. Kiss J.L. Hudson 2004 Adaptive control of unknown unstable steady states of dynamical systems Phys. Rev. E 70 026215 10.1103/PhysRevE.70.026215
58. A. Gjurchinovski V. Urumov 2008 Stabilization of unstable steady states by variable-delay feedback control Europhys. Lett. 84 40013 10.1209/0295-5075/ 84/40013