[Hans Blom, 950509b]
(Bill Powers (950505.0810 MDT))
... You are drawing general conclusions from a
specific design for a method of control. There are other designs.
Yes, I am aware of that. In my demo I concentrated on learning /
system identification. The control part could/should be improved
tremendously before the demo is useful AS A CONTROLLER. But do not
throw out the baby with the bathwater, as the saying goes.
Speaking of real-world demonstrations, are you set up so you could
run a tracking experiment using a mouse as the "control"?
Do to a lack of time, I have to say "no" for now. But I might at a
later time.
This demonstration will directly refute your belief that control
depends on knowledge of "unmodeled dynamics." It does not. This,
too, may take some getting used to...
I have stated in the past, and repeat it now, that any fixed design
controller depends upon knowledge of its world, of the thing to be
controlled, even if that knowledge is hidden and not even visible to
the designer of the system. For a simple example: take your favorite
control system and invert the sign of the way the world reacts.
Control is control no more!
... we can do something constructive by
examining the problem of control with the idea of trying to merge
these two kinds of models.
OK. The basic procedure is simple: use the model-based controller
where it works, and use a conventional controller where it does not.
Implementing this procedure might not be so straightforward,but the
basic idea would be to split the system to be controlled into two
parts, the part that is modelled and the part that is not, and to
apply predictive control to the modelled part PLUS conventional
control to the unmodelled part. I'll start to work on this in my
(little) free time but won't be able to show you something shortly.
If you want to work on this here is the idea: subtract the
predictions of the model from the observations. What is left is the
"unmodelled dynamics" plus noise. Compute a "classical" control
action to control the unmodelled dynamics away. Add this action to
the action computed by the model-based controller. This is ALMOST
what yu do in your next mail:
(Bill Powers (950505.1215 MDT))
The control model subtracts xt (it could have been y, the internal
representation of xt) from xopt to yield an error signal. The
error signal is put through an amplifying leaky integrator to
produce the output variable ("control variable") u.
This is the second part of what I propose. What remains is to combine
BOTH methods.
(Bill Powers (950507.1900 MDT))
In a more sophisticated model, I suppose that the model-correcting
circuitry could be made to search for regular variations in the
perceived output of the real system, and compute some
compensations for them. This, however, would work only for regular
disturbances, and would not work for irregular or arbitrary ones.
There is, potentially, a way of combining a closed-loop model
(which opposes disturbances without needing to know anything about
them) with a model-driven system of the kind Hans has shown us.
However, I am at an impasse in trying to achieve the combination.
I'll work on it.
When the real-world connection is broken, we then want the model
to switch to using the internal world-model as a pseudo-perceptual
signal, exactly as in Hans' model. We would then have the best of
both worlds: the ability to resist arbitrary disturbances in a
simple way when perceptions of the controlled variable are
available, and the ability to continue controlling (in the absence
of disturbances) when perceptual contact with the external world
is lost. I think we can observe BOTH phenomena in behavior, so a
complete model should be able to handle them both.
I fully agree.
The standard PCT model can't handle control when there is a loss
of real-time perceptual information; the adaptive control model of
Hans can't handle control in the presence of arbitrary
disturbances.
However, this "switch" is awkward -- it requires a higher-level
system to detect the loss of the real-time information, and switch
the lower system from using the real-time perception to using the
output of the world-model as the perception.
It need not be a switch; it could be parallel operation. There is
also an unclarity here; my demo has TWO types of "loss of real-time
information". One is where there are no observations, the second is
where there are observations but these do not agree with the model's
predictions. For the latter, there is already a test (the chi-squared
test) to discover them -- and to unlearn and relearn.
(Bill Leach 950507.23:41 U.S. Eastern Time Zone)
[Hans Blom, 950504]
Some of the rest of your posting tends to cause me to believe that
you do not mean this the way that it sounds to me. Control
systems resist ALL disturbances that change perception to the
limits of system output and it matters not if the disturbances are
random, arbitrary or regular in any pattern (such can certainly
influence the success of control but not whether the system will
attempt to resist). Am I 'missing' your point?
Yes, you do. Some of this has been clarified by the ongoing
discussion, I presume. But let me give you a very simple example of a
disturbance that cannot be resisted at all: an impulse disturbance at
an unpredictable time. The disturbance is over before the controller
(any physically realizable controller) can act. If it acts, it acts
inappropriately: the best action is to do nothing. Therefore, optimal
behavior is not to react. This is true for ALL disturbances that are
fully random (unpredictable, white noise) -- but NOT for disturbances
that are somehow regular.
That was my point.
(Rick Marken (950508.0920))
... I think Hans deserves a "wow" for providing
an excellent program that illustrates model-based control; but I
think model- based control doesn't deserve any "wow" at all.
...
Our ordinary control model functions just fine in an environment
in which the disturbance is regular or irregular; Hans model
doesn't function in an environment with ANY disturbance, regular
or irregular.
A question from me to you, long ago, was to demonstrate how your
"ordinary control model" could work fine in a predictable environment
so that it might explain, for instance, the zero reaction times that
are sometimes encountered in those cases. My demo shows zero reaction
times when tracking a square wave, even in noisy environments. Please
show me a demonstration of an ordinary controlmodel that does this
too.
... I think it is very likely that any ability to maintain
apparent control while a perceptual input is briefly lost can
probably be handled by the existing hierarchical control model.
Please demonstrate.
... I think the "prediction" that occurs in control of
imagination can be handled on the input side of a perceptual
control process that uses the perceptual control system that has
last its perception.
Please demonstrate.
But I think we should have some data on control during the
transition from perception to no perception of a controlled
variable before we do much more guessing about the kind of model
that accounts for this (currently make-believe) phenomenon.
I suggested an experiment some time ago: repeatedly make the cursor
briefly invisible in a cursor tracking experiment. This will provide
you with lots and lots of data about this "make-believe phenomenon".
Greetings,
Hans