The Test for Control being Model-Based

[Hans Blom, 960108]

(Bill Powers (951114.1325 MST))

This is much overdue...

How _would_ you test to see if a particular example of behavior
involves model-based control?

The model inside a model-based controller is a summary or simpli-
fication of "the world out there" and is used to predict the
perceptual effects of actions when feedback is missing or very noisy.
Lacking normal perceptual feedback in some modality, or with a very
noisy observation, that modality will still be controlled if a good
enough model is present. In effect, the perception will be provided
by the model, not by the world. Discrimination between model-based
and non-model-based control will be possible only if the "internal
perception" CAN be modelled, i.e. if it is varying in some regular
manner. And this regardless whether the reference level is fixed or
varying, where the latter is undoubtedly the more severe test. The
more severe test is also where the feedback signal is completely
missing for periods of time, rather than just being extra noisy. The
discriminatory power of the test will be highest when there is no
noise in the system.

The Test For Model-Based Control null hypothesis: a model-based
control system's performance will not appreciably degrade when no
feedback is available. (Sloppy formulation, but you get the gist, I
presume. Plenty of qualifications apply, for instance that no model
is perfect and that the period of no feedback should not be too long,
due to the accumulation of prediction error over time).

One example of a practically possible test: ask the subject to
perform some cursor tracking test of a predictable periodic signal
(e.g. square, triangle or sine wave) in which the feedback is
sometimes unavailable, but where the periods where the feedback is
missing are observable, e.g. because the trace on the display
disappears. Otherwise there is no noise. If the subject keeps
tracking more or less satisfactorily, control is model-based. Initial
practice for some time is required to build up the model in the first
place.

The dual-nature "perception" that the subject uses in control is thus
generated by an algorithm of the form

  if feedback available then
    perception := f (action) {f is the world's transfer function}
  else
    perception := g (action) {g is the model's transfer function}

For those who like block diagrams better:

reference r --------------
(varying) ----->|+ |
            p | controller |-----
           ---->|- | |
           > -------------- |
0/1 ---------- |
------>| switch | |
       ---^--^--- |
          > > -------------- |
          > > > > >
          > ---| model |<----
          > pm | (f) | |
          > -------------- | internal
          > > ------------
          > -------------- | external
          > > > >
          ------| world |<---- <-- measurable action
             pw | (g) |

ยทยทยท

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

If the "perception" p is approximately the same regardless whether
feedback from the "world" is available or not (pm ~= pw), we have a
well-behaved model-based controller (g ~= f). Regrettably, we cannot
compare perceptions, but we CAN compare actions. If there is no noise
in the system, actions provide the same information. So, iff the
actions are approximately the same regardless whether feedback is
(temporarily) unavailable or not, we have a well-behaved model-based
controller.

Am I clear?

Greetings,

Hans