Hans' model

[Martin Taylor 950525 11:00]

Bill Powers (950525.0530 MDT)

We can now see that the primary effect of Hans' model is to enable the
controlling system to continue the same pattern of output variations in
the absence of direct sensory feedback from the real controlled
variable. The same result can, I believe, be achieved by a hierarchical
control system.

I have a conjecture, about which I have asked several control engineers
without getting a solid answer:

  For any single-level control system, no matter how complex, there is a
  hierarchical control system made of simple scalar (PCT-standard) elementary
  control systems that behaves the same way as the single-level control
  system, and vice-versa.

This is pure conjecture, so far. Nobody has said that they can show it to
be false or that they can show it to be true. What it means, if true, is
that statements such as "it's not predicting; the effect can be due to
changes in a reference signal from higher levels" are untestable. In the
current discussion, it would mean that the Kalman filter effect might be
obtained equally by reorganization of a structure of simple ECSs.

I have no idea how to test the conjecture, except by counterexample, and
I cannot conceive of a counter-example. But perhaps one of the control
system engineers (active or lurking) on CSG-L might be able to make a
definitive statement on the question.

If it is true, then the important thing is what Bill says:
>It is one thing to design an adaptive control system; it is another to
>show that it is a model of real human behavior.

If both kinds of control system turn out to produce indistinguishable
results, the test (from a PCT viewpoint) is whether their structures can
be discovered in the living thing.



Martin Taylor (950524 14:00) --

    The skilled hunter catches fish. I claim that in doing so he is
    controlling his perceptions. If I understood Rick's earlier
    comment on Hans' posting, Rick would say that if the hunter hits
    the fish with the spear, he is demonstrably NOT controlling his
    perceptions, but is instead controlling an outer-world variable.

He's not controlling the perception you're thinking of, but he's
controlling a perception nonetheless. The perception is "such-and-such
an angle relative to the direction of the fish."

He's controlling many perceptions, and at one level you are no doubt correct.
But just as you have the feeling of "being at the tip" when you feel around
blind with a rod, you also have a feeling of seeing "where the thing is"
when you are practiced in a distorting environment such as through a water
surface. There's no feeling of correcting for the distortion. You just
see it (at least that's the subjective impression). And this sense seems
to map into the words that Hans wrote about what his Kalman filter control
system does (since I can't run it, I can't comment on what it actually does).

Neither the fisher
nor the hunter is capable of aiming at where the fish "actually is" or
where the bird "is going to be."

No, of course not. That's why I suggested to Rick that he should not
despair of PCT if Hans happened to be right. Rick seemed to suggest that
the implication of the model was that the hunter could aim at where it
"actually is."

The controlled perception is an aiming
direction that is in a learned relationship to the perceived direction
of the target.

Like any controlled perception at a level above sensory intensities. The
fact that it is learned does not make it any less a perception. The way
you write it makes it seem like a modification of the output function (which
could be the case, even if it doesn't feel like it when one is in that


[From Rick Marken (950525.0900)]

Bill Powers (950525.0530 MDT) --

I think your assessment of Hans' model still has something wrong with

I think I set about this whole process in the wrong way.

In the post where he posted the code of his "model-based" controller, Hans
Blom (950522) said:

Unmodeled dynamics ARE controlled away by a model-based controller!

I took this as a claim that disturbances (unmodeled dynamics) to an
envionmental variable (xt) could be resisted by a system that was
controlling only a modelled representation of that variable. In other words,
I assumed (incorrectly, it turns out) that Hans' model was controlling a
variable that was NOT a perceptual represenation of xt. However, as you have
shown (and as I suspected from looking at the code) the variable controlled
by the model (x) DOES include the perceptual representation (y) of xt. That

x := x + 0.5*(y - x).

Also, as Hans himself noted in his post, there is no control of xt at all
when the model is blind (y is essentially all noise).

Nevertheless, I proceeded with my analysis of Hans' model under the
assumption that there was little or no contribution of the perception of xt
to the controlled variable, x. So I was not surprised when, after setting the
reference to a constant and applying a disturbance to xt, I found little or
no resistance to the disturbance. Applying a simple version of The Test to
the model showed that it doesn't control.

I did not mean to give Hans' model a hard time; but I didn't go out of my way
to give it an easy time either. I used a constant reference because that
clarified the data plots and I assumed that the model should be able to
control relative to a constant reference if it could control relative to a
varying one. You suggest that a variable reference is needed if the Kalman
filter is to work, in which case the model can reduce the effects of
disturbance by a factor of 10. So Hans' model can control. But it controls
only when it has available a perceptual representaion (y) of the controlled
variable: it can't control blind.

So I was wrong to conclude that Hans' model cannot control. But that mistake
occurred because I assumed that Hans was saying that his model could control
xt without perceiving it. This assumption must have been based on Hans'
other post [Hans Blom (950522b)] where he said:

So, "control of perception" does not apply to model-based control if
the perception is disturbed and the model adjustment algorithm is
given the information that it is.

This seems to be where I got the idea that Hans was saying that xt could be
controlled without a perception of xt. I think we still have to show that the
case that Hans presents as an exception to "control of perception" is not.
Recall that Hans suggested the following experiment:

Experiment: replace

y := xt + normal (vt)

in procedure observe by

y := xt + vt * sin (run/5)

and set vt = 0.5 and pvv = 0.25. For a clearest demonstration set ft
= 0.0 and pff = 0.000001. You will find that after a short learning
period xt (the "world" variable) starts to closely track xopt, but
that the observations y (the blue sine wave line) DO NOT track xopt.

I have not tried this yet but it looks like this is what we should be looking
at. Hans sees this experiment as an exception to the notion that control of a
variable always involves control of a perception of that variable. It looks
like there is control of a real world variable (xt) while the perception (y)
of that variable is ignored. I think we have to show that, if there is
control of xt in this case, then it is a perceptual representation of xt that
is controlled. If we can't show this -- if it is actually true that xt is
controlled while a perceptual reprentation of xt is not -- then I think Hans
has made a monumental discovery.