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### 11.09.2009 - BIRS: Noise, Time Delay and Balance Control

 John Milton Inattention appears to "help" balance Mechanical time-scales matter Stick-balancing appears to be tune to the edge of boundary Don't balance it upright, balance slightly off-center Random walk with an optimal search Non-predictive solution (Maybe stochastic?) Continuous control is too expensive Suggest a discontinuous "act-and-wait" Passive control Better off if you wait to cntrol until stability boundary reached Increased activation delay corresponds to better performance Energy vs Co-energy (How do these correspond to all of the stability studies?) Bob Peterka Observable behavior Kinematics Ground reaction forces EMG response Muscle images ...neural recordings... Experimental and modeling approaches Musculoskeletal dynamics Sensor dynamics Controller Internal models Head vs Trunk (Thomas Mergner) Perception is not perfect Predictors Experiments Used a pseudo-random turning sequence to rotational perturbations Gain and phase of response to rotational perturbations Gain drops off at high frequency Phase leads at low frequency and lags at high frequency Four modes of control Active control Integrative control Fast-acting control Load control Delayed proprioceptive feedback Positive force feedback (force control) Sensory integration feedback (weighted sensory information) Rapid response control (springs and dampers) Valero-Cuevas Cool talks located here: http://bme.usc.edu/valero/ENH/ENH-Schedule.html Levy Flights Long jumps and then a bunch of little jumps One way to get levy flights is to have signal-dependent noise (multiplicative noise) Toro Okihara Stochastic resonance - does the shaking make things better? Perhaps the shaking helps? Non-locality Need to look at components interacting instead of each individual component Ami Radunskaya Delay differential equations $\dot{x} = \sin ( x(t-\tau) )$ Euler's method can be "exact" as long as the step-size directly divides the delay-length dde23 - look-up in matlab What about initial requirements on Laplace equations? $m\ddot{x}(t) +b \dot{x}(t) + q \dot{x}(t-\tau) + k x(t)$ $b^2 = 4 mk$ is critically stable in standard spring-mass-damper b>q the system is stable in this delayed equation To find boundary of stability put in solutions of the form $z(t) = e^{\lambda t}$ Characteristic Polynomial $\lambda^2+b\lambda+q\lambdae^{-\lambda\tau}+k = 0$ Lambda cannot have imaginary solutions with Re>0 If lambda is purely imaginary: $\tau = \frac{1}{\omega}\arctan \left( \frac{\omega^2-k}{\omega b} \right)$Lena TingPostural controlprepatory response (immediate / feedforward)short-latency (stretch reflexes) 40 mslong-latency (automatic postural response) 100 msdecision (steps) 200 ms