model-based control; F(x1..xn)

[From Bill Powers (960305.0100 MST)]

Martin Taylor 960304 15:15 --

What you are calling a "model" includes what I call a "perceptual
function." I do not use "model" that way. This makes for random
relationships between our comments.

     Unless the _whatever-it-is_ can observe the disturbance separately,
     there's no way that regularities in the environmental feedback
     function can be distinguished from regularities in the disturbance

The Artificial Cerebellum does not observe the disturbance separately.
It does not distinguish between, for example, the natural resonant
frequency of a mass on a spring serving as the feedback function and a
periodic force disturbance, or between a periodic force disturbance and
a periodic variation in the reference signal. It can't make that
distinction, and doesn't need to.

As to the rest of this discussion, I can't keep up with it. Put it down
to old age.


Your analysis of hierarchical relationships looks interesting, but I
guess my brain is also having problems with this subject.

     Ignoring the control aspects of the situation, I treated the
     problem as being to determine from incoming data x1,...,xn and the
     value of a function F(x1,...xn) what is the form of that function.

Exactly what function F is it you are talking about? If the environment
consists of x1 ... xn, and the perceptual function is F, then just who
or what is doing the "determining" of the form of this function? You've
jumped into the mathematical development before making it clear just
what you are analyzing.

But go ahead; I'll wait to see how it comes out.

Bill P.