Research‎ > ‎Seminars‎ > ‎Seminars 2009‎ > ‎

### 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 $x_{n+1} = Jx_n + BKSx_n$ 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 motionTRACE-DDE (linear stability analysis for delay-differential equations)Conclusion is that the critical time scale is dominated by the proprioceptive delayAlberte VetteFunctional electrical stimulation (FES)Two major problemsBrain intact, unable to send commandBrain broken, but able to send commandGoal is to help with therapyVette et al Neuromodulation 12, 2009Try and find inverse dynamics for standing postureProblemsMuscle strengtheningDetermine delays between muscle activity to torque generationFound that the delay is around 163 ms Masani et al J Neurophys, 2008Noise and fatigueReverse recruitment of muscle fibersToru OhiraStick balancing through a cart-pendulum.XPP - http://www.enm.bris.ac.uk/staff/hinke/dss/delay/xpp.html