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:
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
- 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
- set
- - 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 |