Skip to main content
SpringerLink
Log in

Time-Delayed Feedback Control

  • Chapter
  • First Online:
Control of Complex Nonlinear Systems with Delay

Part of the book series: Springer Theses ((Springer Theses))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64:1196

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Nijmeijer H, Schaft AVD (1996) Nonlinear dynamical control systems, 3rd edn. Springer, New York

    Google Scholar 

  3. Ogata K (1997) Modern control engineering. Prentice-Hall, New York.

    Google Scholar 

  4. Fradkov AL, Pogromsky AY (1998) Introduction to control of oscillations and chaos. World Scientific, Singapore

    MATH  Google Scholar 

  5. Fradkov AL, Miroshnik IV, Nikiforov VO (1999). Nonlinear and adaptive control of complex systems. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  6. Schuster HG (Editor) (1999) Handbook of chaos control. Wiley-VCH, Weinheim

    MATH  Google Scholar 

  7. Schöll E, Schuster HG (eds) (2008) Handbook of chaos control. Wiley-VCH, Weinheim. Second completely revised and enlarged edition

    Google Scholar 

  8. Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Phys Lett A 170:421

    Article  ADS  Google Scholar 

  9. Socolar JES, Sukow DW, Gauthier DJ (1994) Stabilizing unstable periodic orbits in fast dynamical systems. Phys Rev E 50:3245

    Article  ADS  Google Scholar 

  10. Hövel P, Schöll E (2005) Control of unstable steady states by time-delayed feedback methods. Phys Rev E 72:046203

    Article  Google Scholar 

  11. Sieber J, Krauskopf B (2007) Control based bifurcation analysis for experiments. Nonlinear Dyn 51:365

    Article  MathSciNet  Google Scholar 

  12. Schlesner J (2002) Nichtlineare Oszillationen in Halbleiterübergittern unter zeitverzögerter Rückkopplung. Master’s thesis, Technische Universität Berlin

    Google Scholar 

  13. Schlesner J, Amann A, Janson NB, Just W, Schöll E (2003) Self-stabilization of high frequency oscillations in semiconductor superlattices by time-delay autosynchronization. Phys Rev E 68:066208

    Article  ADS  Google Scholar 

  14. Schlesner J, Amann A, Janson NB, Just W, Schöll E (2004) Self-stabilization of chaotic domain oscillations in superlattices by time-delayed feedback control. Semicond Sci Technol 19:S34

    Article  ADS  Google Scholar 

  15. Kehrt M (2008) Zeitverzögerte Rückkopplungskontrolle eines global gekoppelten Reaktions-Diffusions-Modells. Master’s thesis, Technische Universität Berlin

    Google Scholar 

  16. Hunt BR, Ott E (1996) Optimal periodic orbits of chaotic systems. Phys Rev Lett 76:2254

    Article  ADS  Google Scholar 

  17. Hunt BR, Ott E (1996) Optimal periodic orbits of chaotic systems occur at low period. Phys Rev E 54:328

    Article  ADS  Google Scholar 

  18. Yang T-H, Hunt BR, Ott E (2000) Optimal periodic orbits of continuous time chaotic systems. Phys Rev E 62:1950

    Article  ADS  Google Scholar 

  19. Zoldi SM, Greenside HS (1998) Comment on optimal periodic orbits of chaotic systems. Phys Rev Lett 80:1790

    Article  ADS  Google Scholar 

  20. Hunt BR, Ott E (1998) Hunt and Ott reply. Phys Rev Lett 80:1791

    Article  ADS  Google Scholar 

  21. Just W, Reckwerth D, Möckel J, Reibold E, Benner H (1998) Delayed feedback control of periodic orbits in autonomous systems. Phys Rev Lett 81:562

    Article  ADS  Google Scholar 

  22. Franceschini G, Bose S, Schöll E (1999) Control of chaotic spatiotemporal spiking by time-delay autosynchronisation. Phys Rev E 60:5426

    Article  ADS  Google Scholar 

  23. Zoldi SM, Franceschini G, Bose S, Schöll E (2000) Stabilizing unstable periodic orbits in reaction-diffusion systems by global time-delayed feedback control. In: Fiedler B, Gröger K, Sprekels J (eds) Proceedings of Equadiff 99. World Scientific Publishing, Singapore, p 1311

    Google Scholar 

  24. Yu X (1999) Tracking inherent periodic orbits in chaotic dynamic systems via adaptive variable structure time-delay self control. IEEE Trans Circuits Syst 46:1408

    Article  MATH  Google Scholar 

  25. Ando H, Boccaletti S, Aihara K (2007) Automatic control and tracking of periodic orbits in chaotic systems. Phys Rev E 75:066211

    Article  ADS  Google Scholar 

  26. Pyragas K, Pyragas V, Kiss IZ, Hudson JL (2002) Stabilizing and tracking unknown steady states of dynamical systems. Phys Rev Lett 89:244103

    Article  ADS  Google Scholar 

  27. Parmananda P (2003) Tracking fixed-point dynamics in an electrochemical system using delayed-feedback control. Phys Rev E 67:045202(R)

    Article  ADS  Google Scholar 

  28. Unkelbach J, Amann A, Just W, Schöll E (2003) Time–delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes. Phys Rev E 68:026204

    Article  ADS  Google Scholar 

  29. Schöll E (2004) Pattern formation in semiconductors: control of spatio-temporal dynamics. Ann Phys (Leipzig) 13:403. Special Topic Issue, edited by Friedrich R, Kuhn T, Linz S

    Google Scholar 

  30. Schikora S, Hövel P, Wünsche HJ, Schöll E, Henneberger F (2006) All-optical noninvasive control of unstable steady states in a semiconductor laser. Phys Rev Lett 97:213902

    Article  ADS  Google Scholar 

  31. Schikora S, Wünsche HJ, Henneberger F (2008) All-optical noninvasive chaos control of a semiconductor laser. Phys Rev E 78:025202

    Article  ADS  Google Scholar 

  32. Blakely JN, Illing L, Gauthier DJ (2004) Controlling fast chaos in delay dynamical systems. Phys Rev Lett 92:193901

    Article  ADS  Google Scholar 

  33. Illing L, Gauthier DJ (2005) Hopf bifurcations in time-delay systems with band-limited feedback. Physica D 210:180

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. Sukow DW, Bleich ME, Gauthier DJ, Socolar JES (1997) Controlling chaos in a fast diode resonator using time-delay autosynchronisation: experimental observations and theoretical analysis. Chaos 7:560

    Article  ADS  Google Scholar 

  35. Gauthier DJ, Sukow DW, Concannon HM, Socolar JES (1994) Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization. Phys Rev E 50:2343

    Article  ADS  Google Scholar 

  36. Bleich ME, Socolar JES (1996) Stability of periodic orbits controlled by time-delay feedback. Phys Lett A 210:87

    Article  ADS  Google Scholar 

  37. Bleich ME, Socolar JES (1996) Controlling spatiotemporal dynamics with time-delay feedback. Phys Rev E 54:R17

    Article  ADS  Google Scholar 

  38. Schneider FM, Schöll E, Dahlem MA (2009) Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time delayed feedback. Chaos 19:015110

    Article  ADS  MathSciNet  Google Scholar 

  39. Hövel P, Shah SA, Dahlem MA, Schöll E (2009) Feedback-dependent control of stochastic synchronization in coupled neural systems. In: Fortuna L, Frasca M (eds) Proceedings of 4th international scientific conference on physics and control (PhysCon 09). IPACS Open Access Library http://lib.physcon.ru (e-Library of the International Physics and Control Society), http://arxiv.org/abs/0911.2334v1

  40. Yeung MKS, Strogatz SH. (1999) Time delay in the Kuramoto model of coupled oscillators. Phys Rev Lett 82:648

    Article  ADS  Google Scholar 

  41. Lysyansky B, Maistrenko Y, Tass PA (2008) Coexistence of numerous synchronized and desynchronized states in a model of two phase oscillators coupled with delay. Int J Bifur Chaos 18:1791

    Article  MATH  MathSciNet  Google Scholar 

  42. Rosenblum MG, Pikovsky AS (2004) Controlling synchronization in an ensemble of globally coupled oscillators. Phys Rev Lett 92:114102

    Article  ADS  Google Scholar 

  43. Popovych OV, Hauptmann C, Tass PA (2005) Effective desynchronization by nonlinear delayed feedback. Phys Rev Lett 94:164102

    Article  ADS  Google Scholar 

  44. Popovych OV, Hauptmann C, Tass PA (2005) Demand-controlled desynchronization of brain rhythms by means of nonlinear delayed feedback. In: Proceedings of IEEE Engineering and Medicine Biology. 27th Annual conference

    Google Scholar 

  45. Beck O, Amann A, Schöll E, Socolar JES, Just W (2002) Comparison of time-delayed feedback schemes for spatio-temporal control of chaos in a reaction-diffusion system with global coupling. Phys Rev E 66:016213

    Article  ADS  Google Scholar 

  46. Baba N, Amann A, Schöll E, Just W (2002) Giant improvement of time-delayed feedback control by spatio-temporal filtering. Phys Rev Lett 89:074101

    Article  ADS  Google Scholar 

  47. Just W, Popovich S, Amann A, Baba N, Schöll E (2003) Improvement of time–delayed feedback control by periodic modulation: analytical theory of Floquet mode control scheme. Phys Rev E 67:026222

    Article  ADS  Google Scholar 

  48. Hövel P (2004) Effects of chaos control and latency in time-delay feedback methods. Master’s thesis, Technische Universität Berlin

    Google Scholar 

  49. Schöll E, Hizanidis J, Hövel P, Stegemann G (2007) Pattern formation in semiconductors under the influence of time-delayed feedback control and noise. In: Schimansky-Geier L, Fiedler B, Kurths J, Schöll E (eds) Analysis and control of complex nonlinear processes in physics, chemistry and biology. World Scientific, Singapore, pp 135–183

    Google Scholar 

  50. Stegemann G, Balanov AG, Schöll E (2006) Delayed feedback control of stochastic spatiotemporal dynamics in a resonant tunneling diode. Phys Rev E 73:016203

    Article  ADS  Google Scholar 

  51. Stegemann G, Schöll E (2007) Two-dimensional spatiotemporal pattern formation in the double-barrier resonant tunneling diode. New J Phys 9:55

    Article  Google Scholar 

  52. Hizanidis J, Balanov AG, Amann A, Schöll E (2006) Noise-induced oscillations and their control in semiconductor superlattices. Int J Bifur Chaos 16:1701

    Article  MATH  Google Scholar 

  53. Hizanidis J, Balanov AG, Amann A, Schöll E (2005) Control of noise-induced oscillations in superlattices by delayed feedback. In: Gonzales T, Mateos J, Pardo D (eds) Proceedings of 18th international conference on noise and fluctuations (ICNF-2005), vol 780. American Institute of Physics, Melville, New York), pp 41–44. ISBN 0-7354-0267-1

    Google Scholar 

  54. Hizanidis J, Schöll E (2008) Control of noise-induced spatiotemporal patterns in superlattices. Phys Stat Sol (c) 5:207

    Article  Google Scholar 

  55. Hizanidis J (2008) Control of noise-induced spatio-temporal dynamics in superlattices. Ph.D. thesis, Technische Universität Berlin

    Google Scholar 

  56. Kehrt M, Hövel P, Flunkert V, Dahlem MA, Rodin P, Schöll E (2009) Stabilization of complex spatio-temporal dynamics near a subcritical Hopf bifurcation by time-delayed feedback. Eur Phys J B 68:557

    Article  ADS  MATH  Google Scholar 

  57. Dahms T, Hövel P, Schöll E (2007) Control of unstable steady states by extended time-delayed feedback. Phys Rev E 76:056201

    Article  ADS  MathSciNet  Google Scholar 

  58. Dahms T, Hövel P, Schöll E (2008) Stabilizing continuous-wave output in semiconductor lasers by time-delayed feedback. Phys Rev E 78:056213

    Article  ADS  Google Scholar 

  59. Balanov AG, Janson NB, Schöll E (2005) Delayed feedback control of chaos: bifurcation analysis. Phys Rev E 71:016222

    Article  ADS  Google Scholar 

  60. Just W, Reckwerth D, Reibold E, Benner H (1999) Influence of control loop latency on time-delayed feedback control. Phys Rev E 59:2826

    Article  ADS  Google Scholar 

  61. Hövel P, Socolar JES (2003) Stability domains for time-delay feedback control with latency. Phys Rev E 68:036206

    Article  ADS  Google Scholar 

  62. Manor Y, Koch C, Segev I (1991) Effect of geometrical irregularities on propagation delay in axonal trees. Biophys J 60: 1424

    Article  Google Scholar 

  63. Schwark HD, Jones EG (1989) The distribution of intrinsic cortical axons in area 3b of cat primary somatosensory cortex. Exp Brain Res 78:501

    Article  Google Scholar 

  64. Yousefi M, Lenstra D (1999) Dynamical behavior of a semiconductor laser with filtered external optical feedback. IEEE J Quantum Electron 35:970

    Article  ADS  Google Scholar 

  65. Fischer A, Andersen O, Yousefi M, Stolte S, Lenstra D (2000) Experimental and theoretical study of filtered optical feedback in a semiconductor laser. IEEE J Quantum Electron 36:375

    Article  ADS  Google Scholar 

  66. Lang R, Kobayashi K (1980) External optical feedback effects on semiconductor injection laser properties. IEEE J Quantum Electron 16:347

    Article  ADS  Google Scholar 

  67. Erzgräber H, Krauskopf B, Lenstra D, Fischer APA, Vemuri G (2006) Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback. Phys Rev E 73:055201(R)

    Article  ADS  Google Scholar 

  68. Ahlborn A, Parlitz U (2004) Stabilizing unstable steady states using multiple delay feedback control. Phys Rev Lett 93:264101

    Article  ADS  Google Scholar 

  69. Ahlborn A, Parlitz U (2005) Controlling dynamical systems using multiple delay feedback control. Phys Rev E 72:016206

    Article  ADS  MathSciNet  Google Scholar 

  70. Ahlborn A, Parlitz U (2006) Laser stabilization with multiple-delay feedback control. Opt Lett 31:465

    Article  ADS  Google Scholar 

  71. Ahlborn A, Parlitz U (2007) Controlling spatiotemporal chaos using multiple delays. Phys Rev E 75:65202

    Article  ADS  Google Scholar 

  72. Kyrychko YN, Blyuss KB, Hövel P, Schöll E (2009) Asymptotic properties of the spectrum of neutral delay differential equations. Dyn Sys 24:361

    Article  MATH  Google Scholar 

  73. Blyuss KB, Kyrychko YN, Hövel P, Schöll E (2008) Control of unstable steady states in neutral time-delayed systems. Eur Phys J B 65:571

    Article  ADS  MATH  Google Scholar 

  74. Johnston GA, Hunt ER (1993) Derivative control of the steady state in Chua’s circuit driven in the chaotic region. IEEE Trans Circuits Syst 40:833

    Article  MATH  Google Scholar 

  75. Parmananda P, Rhode MA, Johnson GA, Rollins RW, Dewald HD, Markworth AJ (1994) Stabilization of unstable steady states in an electrochemical system using derivative control. Phys Rev E 49:5007

    Article  ADS  Google Scholar 

  76. Parmananda P, Eiswirth M (1996) Stabilizing unstable fixed points using derivative control. J Phys Chem 100:16568

    Article  Google Scholar 

  77. Lu W, Yu D, Harrison RG (1996) Control of patterns in spatiotemporal chaos in optics. Phys Rev Lett 76:3316

    Article  ADS  Google Scholar 

  78. Dahlem MA, Schneider FM, Schöll E (2008) Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke. Chaos 18:026110

    Article  ADS  MathSciNet  Google Scholar 

  79. Dahlem MA, Hiller G, Panchuk A, Schöll E (2009) Dynamics of delay-coupled excitable neural systems. Int J Bifur Chaos 19:745

    Article  MATH  Google Scholar 

  80. Schneider FM Beeinflussung von neuronalen (2008) Erregungswellen durch raum-zeitliche Rückkopplung., Master’s thesis, Technische Universität Berlin

    Google Scholar 

  81. Guzenko PY, Hövel P, Flunkert V, Fradkov AL, Schöll E (2008) Adaptive tuning of feedback gain in time-delayed feedback control. In: Fradkov A, Andrievsky B (eds) Proceedings of 6th EUROMECH nonlinear dynamics conference (ENOC-2008). IPACS Open Access Library http://lib.physcon.ru (e-Library of the International Physics and Control Society)

  82. Yu X (1997) Tracking inherent periodic orbits in chaotic system via adaptive time delayed self-control. In: Proceedings of the 36th IEEE conference on decision and control vol 1, pp 401

    Google Scholar 

  83. Guzenko PY, Fradkov AL (1997) Gradient control of Henon map dynamics. Int J Bifur Chaos 7:701

    Article  MATH  MathSciNet  Google Scholar 

  84. Fradkov AL, Guzenko PY, Pavlov A (2000) Adaptive control of recurrent trajectories based on linearization of Poincare map. Int J Bifur Chaos 10:621

    MATH  MathSciNet  Google Scholar 

  85. Astrov YA, Fradkov AL, Guzenko PY (2005) Suppression of a noise-induced transition by feedback control. In: Physics and control, 2005. Proceedings 2005 International Conference. IEEE, Piscataway, NJ, US, pp 662–667

    Google Scholar 

  86. Kakmeni FMM, Bowong S, Tchawoua C (2006) Nonlinear adaptive synchronization of a class of chaotic systems. Phys Lett A 355:47

    Article  ADS  Google Scholar 

  87. Liao T-L, Lin S-H (1999) Adaptive control and synchronization of Lorenz systems. J Frankl Inst 336:925

    Article  MATH  MathSciNet  Google Scholar 

  88. Hale JK (1971) Functional differential equations. Applied mathematical sciences, vol 3. Springer, New York

    Book  Google Scholar 

  89. Just W, Bernard T, Ostheimer M, Reibold E, Benner H (1997) Mechanism of time-delayed feedback control. Phys Rev Lett 78:203

    Article  ADS  Google Scholar 

  90. N Baba: Stabilisierung instabiler räumlicher Muster durch zeitverzögerte Rückkopplung mit räumlichen Filtern. Master’s thesis, Technische Universität Berlin (2001)

    Google Scholar 

  91. Amann A, Schöll E, Just W (2007) Some basic remarks on eigenmode expansions of time-delay dynamics. Physica A 373:191

    Article  ADS  Google Scholar 

  92. Wünsche HJ, Schikora S, Henneberger F (2008) Noninvasive control of semiconductor lasers by delayed optical feedback. In:Schöll E, Schuster HG (eds) Handbook of chaos control. Wiley, VCH, Weinheim, second completely revised and enlarged edition

    Google Scholar 

  93. Erzgräber H, Krauskopf B, Lenstra D (2007) Bifurcation analysis of a semiconductor laser with filtered optical feedback. SIAM J Appl Dyn Syst. 6:1

    Article  MATH  MathSciNet  Google Scholar 

  94. Erzgräber H, Lenstra D, Krauskopf B, Fischer APA, Vemuri G (2007) Feedback phase sensitivity of a semiconductor laser subject to filtered optical feedback: experiment and theory. Phys Rev E 76: 026212

    Article  ADS  Google Scholar 

  95. Erzgräber H, Krauskopf B (2007) Dynamics of a filtered-feedback laser: influence of the filter width. Opt Lett 32:2441

    Article  ADS  Google Scholar 

  96. Green K Krauskopf B (2006) Mode structure of a semiconductor laser subject to filtered optical feedback. Opt. Commun. 258:243

    Article  ADS  Google Scholar 

  97. Fischer APA, Yousefi M, Lenstra D, Carter MW, Vemuri G (2004) Filtered optical feedback induced frequency dynamics in semiconductor lasers. Phys Rev Lett 92:023901

    Article  ADS  Google Scholar 

  98. Fischer APA, Yousefi M, Lenstra D, Carter MW, Vemuri G (2004) Experimental and theoretical study of semiconductor laser dynamics due to filtered optical feedback. IEEE J Sel Top Quantum Electron 10:944

    Article  Google Scholar 

  99. Yousefi M, Lenstra D, Vemuri G (2003) Nonlinear dynamics of a semiconductor laser with filtered optical feedback and the influence of noise. Phys Rev E 67:046213

    Article  ADS  Google Scholar 

  100. Illing L, Gauthier DJ (2006) Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback. Chaos 16: 033119

    Article  ADS  Google Scholar 

  101. Wacker A (2002) Semiconductor superlattices: a model system for nonlinear transport. Phys Rep 357:1

    Article  ADS  MATH  Google Scholar 

  102. Amann A (2003) Nonlinear and chaotic front dynamics in semiconductor superlattices. Ph.D. thesis, Technische Unversität Berlin

    Google Scholar 

  103. Wieczorek S, Krauskopf B, Lenstra D (1999) Unifying view of bifurcations in a semiconductor laser subject to optical injection. Opt Commun 172:279

    Article  ADS  Google Scholar 

  104. Krauskopf B, Lenstra D (eds) (2000) Fundamental issues of nonlinear laser dynamics. In: AIP conference proceedings, vol 548. American Institute of Physics, Melville, New York

    Google Scholar 

  105. Wieczorek S, Krauskopf B, Lenstra D (2002) Multipulse excitability in a semiconductor laser with optical injection. Phys Rev Lett 88:063901

    Article  ADS  Google Scholar 

  106. Wieczorek S, Krauskopf B, Simpson T, Lenstra D (2005) The dynamical complexity of optically injected semiconductor lasers. Phys Rep 416:1

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstr. 36, 10623, Berlin, Germany

    Philipp Hövel

Authors
  1. Philipp Hövel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philipp Hövel .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hövel, P. (2010). Time-Delayed Feedback Control. In: Control of Complex Nonlinear Systems with Delay. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14110-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14110-2_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14109-6

  • Online ISBN: 978-3-642-14110-2

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation