stabilization by control

CSGnet Archive CSG1997
1

[Martin Taylor 970107 16:25]

Rick Marken (970107.1300)]

So these words (stabilize and control) _do_ refer to two different
phenomena? The CV in a simulation based control system may be
stabilized (if the system is lucky enoough to have computed the right
outputs) but it is not controlled. The CV in a control system is controlled.
Do I understand correctly now?

Maybe. I would have said "yes" if you had said that the CV in a control
system was stabilized _by being controlled_. That is, taking your definition
of CV:

ยทยทยท

Maybe a better technical definition of CV is "an observer's
representation of the perception controlled by the control system".

-------------

The Tester observes the _environmental_ variable "2x + y", which is
different [from the actual controlled variable: 2.01x + 0.99y].
But 2x + y is stabilized, very nearly as closely as is the true
controlled variable.

This is a question of level of accuracy. It's true that 2.01x + 0.99y isn't
_really_ what is controlled but it's awfully closed to the controlled
variable. If 2.01x + 0.99y were really just stabilized (like the CV in
Bruce's model) then the level of control would go to zero (as measured in
terms of the "Stability measure" I use in the Nature of Control Demo).

No, you are still missing the point. The situation is that you are an
experimenter looking at, and Testing, someone who is _really_ controlling
z' = 2.01x + .99y. You measure the control variability and get an output
vs. disturbance correlation of -0.995. You get a coefficient of stability
of 12.7 (I don't know whether these numbers are compatible, but assume they
are for the sake of argument). You, Mr. Tester, say (using the criterion
in your last message) that the variable you are observing is "controlled."
After all, you have done all the components of the Test, including looking
to see whether the subject can actually sense x and y. You've varied the
disturbances to x and to y all over the lot, and you've got your numbers.
So you are satisfied that what you observed is actually the environmental
correlate of a controlled perception.

But it isn't, because you, Mr. Tester, were observing z = 2x + y. You
found that the value of x wasn't stabilized, or that of y, when you
disturbed either. But z was stabilized, and strongly so. (Aside: in this
situation, x and y are, of course, being controlled, but the output that
is the control action for z varies the reference levels for both, so neither
stabilizes when disturbed).

Now let's change the situation and add that pesky "w" that you, Mr Tester,
know nothing of. (This is a new Subject, and a new experiment). The Subject
is _really_ controlling z' = 2.01x + 0.99y + .003w. (Since we are the
gods that created the Subject, we know this). You measure, do the Test,
and get a correlation of -0.995 and a coefficient of stability of 12.7. Are
you justified in saying that what you were observing (z == 2x + y) is
controlled? Your Test results say it is, but as we gods know, you've missed
an entire dimension that's involved in what is _really_ controlled. (As
well as getting the coefficients slightly wrong).

Now you retest the same subject, and this time, w fluctuates during the test.
You get an output-disturbance correlation of 0.987 and a stability index
of 10.8. It's not as good as before, but do you decide you were looking at
an uncontrolled variable? Not if the discussions on CSGnet over the last
few years are anything to go by. And not only do you not know that w is
involved, you don't even know that w _exists_. Why should you not be happy
that you have found a controlled variable?
-----------------
In all of this I would say that you would be correct to say that you are
observing a variable that is being stabilized by control, but wrong to say
you are observing a controlled variable.

This is why I prefer to talk about observable (environmental) variables
being "stabilized" whereas perceptual variables (and their environmental
correlates, that one can never know one is observing) are "controlled."

It's a distinction that goes well beyond the question of whether the
stability is due to control or to model-based outflow patterning of actions.

Martin

2

[From Rick Marken (970107.1515)]

Martin Taylor (970107 16:25) --

The situation is that you are an experimenter looking at, and
Testing, someone who is _really_ controlling z' = 2.01x + .99y. You
measure the control variability and get an output vs. disturbance
correlation of -0.995. You get a coefficient of stability of
12.7...You, Mr. Tester, say...that the variable you are observing
is "controlled."

I sure do.

But it isn't, because you, Mr. Tester, were observing z = 2x + y.

Yes. But my estimate of the controlled variable based on The Test is
sure CLOSE to the real one. In our tracking tasks it looks like the
position of the cursor (x) is controlled. But it may actually be
x+.0001*x is _really_ controlled. But who cares? It's a difference that
doesn;t make a difference.

Now let's change the situation and add that pesky "w" that you, Mr
Tester, know nothing of...The Subject is _really_ controlling
z' = 2.01x + 0.99y + .003w...You measure, do the Test, and get a
...coefficient of stability of 12.7. Are you justified in saying
that what you were observing (z == 2x + y) is controlled? Your Test
results say it is, but as we gods know, you've missed an entire
dimension that's involved in what is _really_ controlled.

Of course. You Gods might not think so but I sure do.

Now you retest the same subject, and this time, w fluctuates...You
get an output-disturbance correlation of 0.987 and a stability index
of 10.8. It's not as good as before, but do you decide you were
looking at an uncontrolled variable? Not if the discussions on
CSGnet over the last few years are anything to go by.

Right. We decide that we are _not_ looking at an uncontrolled variable
because the measure of control is still 10 standard deviations higher
than what we would expect to get if there were no control. What we
decide
is that we do not have the _exactly correct_ definition of the
controlled variable; but we have one that is _pretty darn good_. If we
think we need
to have a better definition of the controlled variable -- so that the
measure of control is even higher -- then we keep doing The Test. We do
not -- repeat, we do not -- retreat to the ivory tower to _think about_
what variable might _really_ be controlled.

Why should you not be happy that you have found a controlled
variable?

You got me. If I were monitoring a variable that had a stability index
of 10.8 I'd feel pretty confident that I was looking at something that
was
_one hell of a lot_ like the actual controlled variable -- and the Gods
be damned;-)

This is why I prefer to talk about observable (environmental)
variables being "stabilized" whereas perceptual variables (and
their environmental correlates, that one can never know one is
observing) are "controlled."

Yikes! This statement makes sense to me;-)

This is OK with me. But then I wonder what we should call behavior like
that of the enviromental variable ("CV") in Bruce's simulation-based
control model; the "CV" in that model was maintained at a fixed value
(as long as the model was computing the correct outputs) but was not
"stabilized" (by your meaning of "stabilized" above) and it was not
controlled (again because, by your definition above, only perceptions
are controlled).

It seems to me that your distinction between "stabilized" and
"controlled" is an attempt to remind people that The Test for the
Controlled Variable does not reveal THE ACTUAL variable that corresponds
to the perception being controlled by the control system. This is a
worthwhile reminder. But I think it would be better to reserve the word
"stabilize" for behavior like that of the CV in Bruce's simulation-based
control model. We could make the point you want to make by simply saying
that The Test provides an arbitrarily accurate
ESTIMATE of the perceptual variable that is under control. How about
that?

Best

Rick