Biological Cybernetics

, Volume 104, Issue 1–2, pp 31–51 | Cite as

Intermittent control: a computational theory of human control

  • Peter Gawthrop
  • Ian Loram
  • Martin Lakie
  • Henrik Gollee
Original Paper


The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as “continuous observation, intermittent action”. Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.


Intermittent control Predictive control Optimal control Human operator Human balancing 


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  1. Asai Y, Tasaka Y, Nomura K, Nomura T, Casadio M, Morasso P (2009) A model of postural control in quiet standing: robust compensation of delay-induced instability using intermittent activation of feedback control. PLoS One 4(7): e6169PubMedCrossRefGoogle Scholar
  2. Baron S, Kleinman DL (1969) The human as an optimal controller and information processor. IEEE Trans Man-Machine Syst 10(1): 0 9–17CrossRefGoogle Scholar
  3. Baron S, Kleinman DL, Levison WH (1970) An optimal control model of human response part II: prediction of human performance in a complex task. Automatica 6(3): 371–383CrossRefGoogle Scholar
  4. Barry S (1979) Functional integration and quantum physics. Academic Press, New YorkGoogle Scholar
  5. Barto AG, Fagg AH, Sitkoff N, Houk JC (1999) A cerebellar model of timing and prediction in the control of reaching. Neural Comput 11(3): 565–594PubMedCrossRefGoogle Scholar
  6. Bays PM, Wolpert DM (2007) Computational principles of sensorimotor control that minimize uncertainty and variability. J Physiol 578(Pt 2): 387–396PubMedGoogle Scholar
  7. Bays PM, Wolpert DM, Flanagan JR (2005) Perception of the consequences of self-action is temporally tuned and event driven. Curr Biol 15(12): 1125–1128PubMedCrossRefGoogle Scholar
  8. Bekey GA (1962) The human operator as a sampled-data system. IRE Trans Human Factors Electron HFE-3(2): 43–51CrossRefGoogle Scholar
  9. Ben-Itzhak S, Karniel A (2008) Minimum acceleration criterion with constraints implies bang-bang control as an underlying principle for optimal trajectories of arm reaching movements. Neural Comput 20(3): 779–812PubMedCrossRefGoogle Scholar
  10. Bhushan N, Shadmehr R (1999) Computational nature of human adaptive control during learning of reaching movements in force fields. Biol Cybern 81(1): 39–60PubMedCrossRefGoogle Scholar
  11. Burdet E, Milner TE (1998) Quantization of human motions and learning of accurate movements. Biol Cybern 78(4): 307–318PubMedCrossRefGoogle Scholar
  12. Bye RT, Neilson PD (2008) The BUMP model of response planning: variable horizon predictive control accounts for the speed-accuracy tradeoffs and velocity profiles of aimed movement. Hum Mov Sci 27(5): 771–798PubMedCrossRefGoogle Scholar
  13. Craik KJW (1947) Theory of the human operator in control systems. I. The operator as an engineering system. Br J Psychol Gen Sect 38(Pt 2): 56–61PubMedGoogle Scholar
  14. Craik KJW (1948) Theory of the human operator in control systems. II: man as an element in a control system. Br J Psychol Gen Sect 38(Pt 3): 142–148PubMedGoogle Scholar
  15. Davidson PR, Wolpert DM (2005) Widespread access to predictive models in the motor system: a short review. J Neural Eng 2(3): S313–S319PubMedCrossRefGoogle Scholar
  16. Dean P, Porrill J (2008) Adaptive-filter models of the cerebellum: computational analysis. Cerebellum 7(4): 567–571PubMedCrossRefGoogle Scholar
  17. Doeringer JA, Hogan N (1998) Serial processing in human movement production. Neural Netw 11(7–8): 1345–1356PubMedCrossRefGoogle Scholar
  18. Estrada T, Antsaklis PJ (2008) Stability of discrete-time plants using model-based control with intermittent feedback. In: Proceedings of the 16th Mediterranean Conference on Control and Automation, June 2008, pp 1130–1136Google Scholar
  19. Fitzpatrick R, McCloskey DI (1994) Proprioceptive, visual and vestibular thresholds for the perception of sway during standing in humans. J Physiol 478(Pt 1): 173–186PubMedGoogle Scholar
  20. Franklin GF, Powell JD, Emami-Naeini A (1994) Feedback control of dynamic systems, 3rd edn. Addison-Wesley, BostonGoogle Scholar
  21. Gawthrop PJ (2002) Physical model-based intermittent predictive control. In: Kaczorek T (ed) Proceedings of the 8th IEEE International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, September 2002, pp 707–712Google Scholar
  22. Gawthrop PJ (2004) Intermittent constrained predictive control of mechanical systems. In: Petersen IR (ed) Proceedigns of the 3rd IFAC Symposium on Mechatronic Systems, Manly, AustraliaGoogle Scholar
  23. Gawthrop PJ (2009) Frequency domain analysis of intermittent control. Proc Inst Mech Eng Pt I: J Syst Control Eng 223(5): 591–603CrossRefGoogle Scholar
  24. Gawthrop PJ (2010) Act-and-wait and intermittent control: some comments. IEEE Trans Control Syst Technol 18(5): 1195–1198CrossRefGoogle Scholar
  25. Gawthrop PJ, Wang L (2006) Intermittent predictive control of an inverted pendulum. Control Eng Pract 14(11): 1347–1356CrossRefGoogle Scholar
  26. Gawthrop PJ, Wang L (2007) Intermittent model predictive control. Proc Inst Mech Eng Pt I: J Syst Control Eng 221(7): 1007–1018CrossRefGoogle Scholar
  27. Gawthrop PJ, Wang L (2009) Event-driven intermittent control. Int J Control 82(12): 2235–2248CrossRefGoogle Scholar
  28. Gawthrop P, Loram I, Lakie M (2009) Predictive feedback in human simulated pendulum balancing. Biol Cybern 101(2): 131–146PubMedCrossRefGoogle Scholar
  29. Gollee H, Mamma A, Loram I, Gawthrop PJ (2010) Frequency-domain identification of the human controller. Unpublished msGoogle Scholar
  30. Goodwin GC, Graebe SF, Salgado ME (2001) Control system design. Prentice Hall, Englewood, NJGoogle Scholar
  31. Hanneton S, Berthoz A, Droulez J, Slotine JJ (1997) Does the brain use sliding variables for the control of movements?. Biol Cybern 77(6): 381–393PubMedCrossRefGoogle Scholar
  32. Hoff B, Arbib MA (1993) Models of trajectory formation and temporal interaction of reach and grasp. J Mot Behav 25(3): 175–192PubMedCrossRefGoogle Scholar
  33. Insperger T (2006) Act-and-wait concept for continuous-time control systems with feedback delay. IEEE Trans Control Syst Technol 14(5): 974–977CrossRefGoogle Scholar
  34. Karniel A, Inbar GF (1997) A model for learning human reaching movements. Biol Cybern 77(3): 173–183PubMedCrossRefGoogle Scholar
  35. Kleinman D (1969) Optimal control of linear systems with time-delay and observation noise. IEEE Trans Autom Control 14(5): 524–527CrossRefGoogle Scholar
  36. Kleinman DL, Baron S, Levison WH (1970) An optimal control model of human response. Part I: theory and validation. Automatica 6(3): 357–369CrossRefGoogle Scholar
  37. Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley, New YorkGoogle Scholar
  38. Levison WH, Baron S, Kleinman DL (1969) A model for human controller remnant. IEEE Trans Man-Machine Syst 10(4): 101–108CrossRefGoogle Scholar
  39. Lewis PA, Miall RC (2009) The precision of temporal judgement: milliseconds, many minutes, and beyond. Philos Trans R Soc B: Biol Sci 364(1525): 1897–1905CrossRefGoogle Scholar
  40. Lockhart DB, Ting LH (2007) Optimal sensorimotor transformations for balance. Nat Neurosci 10(10): 1329–1336PubMedCrossRefGoogle Scholar
  41. Loewenstein Y, Mahon S, Chadderton P, Kitamura K, Sompolinsky H, Yarom Y, Häusser Ml (2005) Bistability of cerebellar purkinje cells modulated by sensory stimulation. Nat Neurosci 8(2): 202–211PubMedCrossRefGoogle Scholar
  42. Loram ID, Lakie M (2002) Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements. J Physiol 540(Pt 3): 1111–1124PubMedCrossRefGoogle Scholar
  43. Loram ID, Maganaris CN, Lakie M (2005a) Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius. J Physiol 564(Pt 1): 295–311PubMedCrossRefGoogle Scholar
  44. Loram ID, Maganaris CN, Lakie M (2005b) Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced. J Physiol 564(Pt 1): 281–293PubMedCrossRefGoogle Scholar
  45. Loram ID, Lakie M, Gawthrop PJ (2009) Visual control of stable and unstable loads: what is the feedback delay and extent of linear time-invariant control?. J Physiol 587(Pt 6): 1343–1365PubMedCrossRefGoogle Scholar
  46. Marr D (1982) Vision. A computational investigation into the human representation and processing of visual information. W. H. Freeman, San FranciscoGoogle Scholar
  47. Maurer C, Peterka RJ (2005) A new interpretation of spontaneous sway measures based on a simple model of human postural control. J Neurophysiol 93(1): 189–200PubMedCrossRefGoogle Scholar
  48. McLeod P (1977) Parallel processing and the psychological refractory period. Acta Psychol 41(5): 381–396CrossRefGoogle Scholar
  49. McRuer D (1980) Human dynamics in man-machine systems. Automatica 16(3): 237–253CrossRefGoogle Scholar
  50. Miall RC, Wolpert DM (1996) Forward models for physiological motor control. Neural Netw 9(8): 1265–1279PubMedCrossRefGoogle Scholar
  51. Miall RC, King D (2008) State estimation in the cerebellum. Cerebellum 7(4): 572–576PubMedCrossRefGoogle Scholar
  52. Miall RC, Weir DJ, Stein JF (1993a) Intermittency in human manual tracking tasks. J Mot Behav 25(1): 53–63PubMedCrossRefGoogle Scholar
  53. Miall RC, Weir DJ, Wolpert DM, Stein JF (1993b) Is the cerebellum a Smith predictor. J Mot Behav 25(3): 203–216PubMedCrossRefGoogle Scholar
  54. Navas F, Stark L (1968) Sampling or intermittency in hand control system dynamics. Biophys J 8(2): 252–302PubMedCrossRefGoogle Scholar
  55. Navon D, Miller J (2002) Queuing or sharing? A critical evaluation of the single-bottleneck notion. Cogn Psychol 44(3): 193–251PubMedCrossRefGoogle Scholar
  56. Neilson PD (1999) Influence of intermittency and synergy on grasping. Motor Control 3(3):280–284 (discussion 316–25)Google Scholar
  57. Neilson PD, Neilson MD (1999) A neuroengineering solution to the optimal tracking problem. Hum Mov Sci 18(2–3): 155–183CrossRefGoogle Scholar
  58. Neilson PD, Neilson MD (2005) An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control. J Neural Eng 2(3): S279–S312PubMedCrossRefGoogle Scholar
  59. Neilson PD, Neilson MD, O’Dwyer NJ (1988) Internal models and intermittency: a theoretical account of human tracking behavior. Biol Cybern 58(2): 101–112PubMedCrossRefGoogle Scholar
  60. Novak KE, Miller LE, Houk JC (2002) The use of overlapping submovements in the control of rapid hand movements. Exp Brain Res 144(3): 351–364PubMedCrossRefGoogle Scholar
  61. Oytam Y, Neilson PD, O’Dwyer NJ (2005) Degrees of freedom and motor planning in purposive movement. Hum Mov Sci 24(5–6): 710–730PubMedCrossRefGoogle Scholar
  62. Peterka RJ (2002) Sensorimotor integration in human postural control. J Neurophysiol 88(3): 1097–1118PubMedGoogle Scholar
  63. Pew RW, Duffendack JC, Fensch LK (1967) Sine-wave tracking revisited. IEEE Trans Human Factors Electron HFE-8(2): 130–134CrossRefGoogle Scholar
  64. Ronco E, Arsan T, Gawthrop PJ (1999) Open-loop intermittent feedback control: practical continuous-time GPC. IEE Proc Part D: Control Theory Appl 146(5): 426–434CrossRefGoogle Scholar
  65. Shadmehr R, Wise SP (2005) Computational neurobiology of reaching and pointing: a foundation for motor learning. MIT Press, CambridgeGoogle Scholar
  66. Smith MC (1967) Theories of the psychological refractory period. Psychol Bull 67(3): 202–213PubMedCrossRefGoogle Scholar
  67. Stanley J, Miall RC (2009) Using predictive motor control processes in a cognitive task: behavioral and neuroanatomical perspectives. Adv Exp Med Biol 629: 337–354PubMedCrossRefGoogle Scholar
  68. Telford CW (1931) The refractory phase of voluntary and associative responses. J Exp Psychol 14(1): 1–36CrossRefGoogle Scholar
  69. Todorov E, Jordan MI (2002) Optimal feedback control as a theory of motor coordination. Nat Neurosci 5(11): 1226–1235PubMedCrossRefGoogle Scholar
  70. van der Kooij H, de Vlugt E (2007) Postural responses evoked by platform pertubations are dominated by continuous feedback. J Neurophysiol 98(2): 730–743PubMedCrossRefGoogle Scholar
  71. van der Kooij H, Jacobs R, Koopman B, Grootenboer H (1999) A multisensory integration model of human stance control. Biol Cybern 80(5): 299–308PubMedCrossRefGoogle Scholar
  72. van der Kooij H, Jacobs R, Koopman B, van der Helm F (2001) An adaptive model of sensory integration in a dynamic environment applied to human stance control. Biol Cybern 84(2): 103–115PubMedCrossRefGoogle Scholar
  73. Vince MA (1948) The intermittency of control movements and the psychological refractory period. Br J Psychol Gen Sect 38(Pt 3): 149–157PubMedGoogle Scholar
  74. Welch TDJ, Ting LH (2008) A feedback model reproduces muscle activity during human postural responses to support-surface translations. J Neurophysiol 99(2): 1032–1038PubMedCrossRefGoogle Scholar
  75. Welford AT (1967) Single-channel operation in the brain. Acta Psychol (Amst) 27: 5–22CrossRefGoogle Scholar
  76. Wickens CD, Hollands JG (2000) Engineering psychology and human performance, 3rd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  77. Wolpert DM, Ghahramani Z, Jordan MI (1995) An internal model for sensorimotor integration. Science 269(5232): 1880–1882PubMedCrossRefGoogle Scholar
  78. Wolpert DM, Miall RC, Kawato M (1998) Internal models in the cerebellum. Trends Cogn Sci 2(9): 338–347PubMedCrossRefGoogle Scholar
  79. Woodworth R (1899) The accuracy of voluntary movement. Psychol Rev 3: 1–114Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Peter Gawthrop
    • 1
  • Ian Loram
    • 2
  • Martin Lakie
    • 3
  • Henrik Gollee
    • 1
  1. 1.School of EngineeringUniversity of GlasgowGlasgowUK
  2. 2.Institute for Biomedical Research into Human Movement and HealthManchester Metropolitan UniversityManchesterUK
  3. 3.School of Sport and Exercise SciencesThe University of BirminghamBirmingham, EdgbastonUK

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