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Might there be a theory as to how organisms are dynamically stable? If mammals model dynamics using piece-wise linear functions, then we know that almost all square matrices are invertible so an inverse exists locally.
cc: @GunnarBlohm, @JCashaback, @KordingLab, @JonAMichaels
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Aidan Rocke
@bayesianbrain
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I am pretty confident this idea has been explored so I am curious about references.
I think such a theory should work for pretty complex inverse dynamics since the composition of a sequence of invertible functions is also invertible.
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Aidan Rocke
@bayesianbrain
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Concerning the almost-all property the way this helps is that if we have a deterministic controller F that is piece-wise linear and each Jacobian is square, we only have to add gaussian noise ~N(0,epsilon) to this Jacobian so that F is locally invertible with probability one.
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