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
    • http://twr.cs.kuleuven.be/research/software/delay/ddebiftool.shtml
    • 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
K = -B^{-1}JS^{-1}
        • set
BKSx_n
KSx_n
Sx_n
        • - action on system - scaling of activation - 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