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11.10.2009 - BIRS: Noise, Time Delay and Balance Control

Jan Sieber
  • There are some conditions in which you can take an unstable linear system and adding noise can stabilize the system.
  • An equivalent "eig" function can be found in DDE-BIFTOOL
  • Using delay equations appears to be an approximation of "spatial variables"
    • Delay equations may be an easier way to express wave-phenomena
  • Sources of discontinuity
    • Friction
    • Finite sampling (space = chaos, time = act-and-wait can stabilize)
    • Switching between discrete state
  • Switching control based on a return map of:
    • Space
    • Time
    • Phase-space
Rachel Kuske
  • Competition of noise sources in delay dynamics
    • Noise in parameters
    • Noise in delay
  • Coherence resonance
    • Adding noise to the system can induce a conditional "oscillation"
    • Adding noise to the system can induce oscillations with amplitude magnified greater than the noise amplitude
  • Bifurcations
    • Sub-critical
      • small oscillation state bifurcates to a large oscillation state
    • Super-critical
      • Tend to be stable?
    • Hopf bifurcation
      • Stable fixed point splits to a saddle node
  • Phenomena with noise can be modeled completely deterministically, so how do you know which model is better?
    • Check out the bifurcation diagrams, as they have different structures
Andy Ruina
  • Deadbeat control: Things you should know, but don't
  • Passive dynamics - not stable enough
  • Reflex control - too much guess work
  • Optimal feedback - too much complexity vs pay-off
  • Control Theory
    • If sensor delay is greater than characteristic delay, system is unstable
    • x_{n+1} = Jx_n + BKSx_n
      • set K = -B^{-1}JS^{-1}
      • BKSx_n - action on system
      • KSx_n - scaling of activation
      • Sx_n - sensor state
Jason Boulet
  • Werness and Anderson (1984) - Stiffness properties measured
  • Hurst exponent has to be greater than 0.5 for it to be Brownian motion
  • TRACE-DDE (linear stability analysis for delay-differential equations)
  • Conclusion is that the critical time scale is dominated by the proprioceptive delay
Alberte Vette
  • Functional electrical stimulation (FES)
  • Two major problems
    • Brain intact, unable to send command
    • Brain broken, but able to send command
  • Goal is to help with therapy
    • Vette et al Neuromodulation 12, 2009
      • Try and find inverse dynamics for standing posture
  • Problems
    • Muscle strengthening
    • Determine delays between muscle activity to torque generation
      • Found that the delay is around 163 ms Masani et al J Neurophys, 2008
    • Noise and fatigue
      • Reverse recruitment of muscle fibers
Toru Ohira