Balancing with Noise and Delay

Hosaka, Tadaaki; Ohira, Toru; Luciani, Christian; Cabrera, Juan Luis; Milton, John

doi:10.1143/ptps.161.314

Cited by 13 publications

(11 citation statements)

References 22 publications

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“…The conclusion that position control feedback is positive also arises in studies of the closely related task of stick balancing at the fingertip [10,11,[22][23][24][25][26]. During stick balancing the nervous system strives to minimize the vertical displacement angle.…”

mentioning

confidence: 99%

Unstable dynamical systems: Delays, noise and control

Milton¹,

Cabrera²,

Ohira³

2008

Europhys. Lett.

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Escape from an unstable fixed point in a time-delayed dynamical system in the presence of additive white noise depends on both the magnitude of the time delay, τ , and the initial function. In particular, the longer the delay the smaller the variance and hence the slower the rate of escape. Numerical simulations demonstrate that the distribution of first passage times is bimodal, the longest first passage times are associated with those initial functions that cause the greatest number of delayed zero crossings, i.e. instances where the deviations of the controlled variable from the fixed point at times t and t − τ have opposite signs. These observations support the utility of control strategies using pulsatile stimuli triggered only when variables exceed certain thresholds.

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mentioning

confidence: 99%

Unstable dynamical systems: Delays, noise and control

Milton¹,

Cabrera²,

Ohira³

2008

Europhys. Lett.

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“…For example, novice stick balancers are capable of improving performance, i.e. shift the stick survival curve to the right, by concurrently moving a leg rhythmically [15]. The fact that a similar improvement in performance can be obtained by having the subject think about moving the leg rhythmically, but not actually moving it [16], demonstrates that this improvement is not simply due to mechanical vibrations of the fingertip induced by leg movement.…”

Section: Discussionmentioning

confidence: 99%

“…To address this question we have considered the case of the repulsive delayed random walk [15] which, in turn, is a special case of the delayed random walk (DRW) [34]. In the DRW the walker takes a discrete step of unit length per unit time in a direction determined by a set of conditional probabilities that depend on the position of the walker at a given time in the past, τ .…”

Section: Stabilizing With Noise and Delaymentioning

confidence: 99%

“…Thus the intriguing question for stick balancing is not why the stick can be balanced at the fingertip, but to understand why the balanced stick eventually falls! Here we review our studies on stick balancing at the fingertip [2,6,[12][13][14][15][16]. We demonstrate that it is possible to gain insight into the nature of the control strategy used by the nervous system by carefully studying the statistical properties of the fluctuations made in the controlled variable, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Neural control on multiple time scales: Insights from human stick balancing

Cabrera¹,

Luciani²,

Milton³

2006

Condens. Matter Phys.

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The time-delayed feedback control mechanisms of the nervous system are continuously subjected to the effects of uncontrolled random perturbations (herein referred to as noise). In this setting the statistical properties of the fluctuations in the controlled variable(s) can provide non-invasive insights into the nature of the underlying control mechanisms. We illustrate this concept through a study of stick balancing at the fingertip using high speed motion capture techniques. Experimental observations together with numerical studies of a stochastic delay differential equation demonstrate that on time scales short compared to the neural time delay ("fast control"), parametric noise provides a non-predictive mechanism that transiently stabilizes the upright position of the balanced stick. Moreover, numerical simulations of a delayed random walker with a repulsive origin indicate that even an unstable fixed point can be transiently stabilized by the interplay between noise and time delay. In contrast, on time scales comparable to the neural time delay ("slow control"), feedback and feedforward control mechanisms become more important. The relative contribution of the fast and slow control mechanisms to stick balancing is dynamic and, for example, depends on the context in which stick balancing is performed and the expertise of the balancer.

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“…However, careful experimental observations for postural sway [38,39] and stick balancing at the fingertip [11,12,28] indicate that the feedback is on average positive and that it is administered in a pulsatile, or ballistic, manner. Recently the following switch-type discontinuous model for postural sway that incorporates positive feedback has been introduced in an attempt to resolve this paradox [49,50]:…”

Section: Balance Control With Positive Feedbackmentioning

confidence: 99%

Delayed Random Walks: Investigating the Interplay Between Delay and Noise

Ohira

Milton

2009

Delay Differential Equations

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Summary.A model for a 1-dimensional delayed random walk is developed by generalizing the Ehrenfest model of a discrete random walk evolving on a quadratic, or harmonic, potential to the case of non-zero delay. The Fokker-Planck equation derived from this delayed random walk (DRW) is identical to that obtained starting from the delayed Langevin equation, i.e. a first-order stochastic delay differential equation (SDDE). Thus this DRW and SDDE provide alternate, but complimentary ways for describing the interplay between noise and delay in the vicinity of a fixed point. The DRW representation lends itself to determinations of the joint probability function and, in particular, to the auto-correlation function for both the stationary and transient states. Thus the effects of delay are manisfested through experimentally measurable quantities such as the variance, correlation time, and the power spectrum. Our findings are illustrated through applications to the analysis of the fluctuations in the center of pressure that occur during quiet standing.Key words: delay, random walk, stochastic delay differential equation, Fokker-Planck equation, auto-correlation function, postural sway Feedback control mechanisms are ubiquitous in physiology [2,8,17,22,34,41,47,48,60,63,65,66,67]. There are two important intrinsic features of these control mechanisms: 1) all of them contain time delays; and 2) all of them are continually subjected to the effects of random, uncontrolled fluctuations (herein referred to as "noise"). The presence of time delays is a consequence of the simple fact that the different sensors that detect changes in the controlled variable and the effectors that act on this variable are spatially distributed. Since transmission and conduction times are finite, time delays are unavoidable. As a consequence, mathematical models for feedback control take the form of stochastic delay differential equations (SDDE); an example is the delayed Langevin equation or first-order SDDE with additive noise [20,25,33,36,37,42,43,53,59] dx(t) = −kx(t − τ )dt + dW(1)

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Balancing with Noise and Delay

Cited by 13 publications

References 22 publications

Unstable dynamical systems: Delays, noise and control

Unstable dynamical systems: Delays, noise and control

Neural control on multiple time scales: Insights from human stick balancing

Delayed Random Walks: Investigating the Interplay Between Delay and Noise

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