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

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
- 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?

$\dot{x} = \sin ( x(t-\tau) )$

$m\ddot{x}(t) +b \dot{x}(t) + q \dot{x}(t-\tau) + k x(t)$

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
- Characteristic Polynomial
  - Lambda cannot have imaginary solutions with Re>0
  - If lambda is purely imaginary:

$z(t) = e^{\lambda t}$

$\tau = \frac{1}{\omega}\arctan \left( \frac{\omega^2-k}{\omega b} \right)$

Lena Ting

Postural control
- prepatory response (immediate / feedforward)
- short-latency (stretch reflexes) 40 ms
- long-latency (automatic postural response) 100 ms
- decision (steps) 200 ms

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