Control, Model-based behavior

[From Rick Marken (950512.0930)]

Bill Powers (950511.0800 MDT) --

It's hard to get people to take the basic control-of-input principle as
a premise, and explore how to use it in explaining unusual modes of
behavior.

I saw this post from Bill AFTER I [Rick Marken (950511.1330)] posted the
following to Bill Leach:

If the control view of behavior were taken for granted, then I would have no
problem with the discussion of "model- based" control; some kind of "model-
based" control is surely involved when you move your hand towards the
currently invisible soap,

In other words, both Bill and I have a problem with this "model based
control" thread because it's hard enough trying to get people to enter the
PCT "big top" without offering an amusing "side show". Model based "control"
is certainly interesting, but it is not of fundamental significance. Still,
it does seem to contradict the idea of control of perception so I guess we
have to keep dealing with it. And, as Oded Maler (950512) says

It might be that this "shampoo in the eyes" situation is much more common
than you seem to admit.

Since it looks like we are going to have "model based control" with us for a
while, let me make two points that will (hopefully) clarify the issue a bit.

1) There is no control without perception.

I hope we can agree that there is no "control" (in the PCT sense) when
there is no perception of the variable under control. When you reach for the
soap with eyes closed there is no visual variable under control. The same is
true in the tracking tasks; when the target or cursor becomes invisible, the
visual relationship between target and cursor (the variable that had been
under control) is no longer under control.

So the term "model based control" is really an oxymoron; a model might help
generate actions (reaching for soap, moving the mouse) that make it look (to
an observer) like some variable (hand/soap relationship, target/cursor
relationship) is under control; but a variable is (demonstrably) NOT under
control when it is not perceived. I think we should stop talking about "model
based control" because it is misleading (there is no control); I suggest we
refer to it as "model-based behavior" since "behavior" is more ambiguous
than control since it can refer to non- controlled as well as controlled
results of action.

2) Control of imagination vs model based behavior

I think we have to clearly discriminate between "model based behavior" and
"control of imagination". Bill Powers (950512.0100 MDT) just posted a verbal
description of the difference:

Model-based control doesn't mean repeating specific signals that have
occurred in the past. It means constructing a model with a structure
that will create signals like those that the real environment would
create, given any actions on the environment.

Here is a graphical representation of the difference:

                    >
                    r
                    v
          p------| |------e
          ^ |
          > >
        > s | <--|f'()|-----| o | System
..................................................
          ^ | Environment
          > v
   d ---> qi <----|f()|-------|

This is the basic control system with an added internal connection between
the output function (o) and input function (i). This internal connection is
the "imagination connection"; in B:CP this connection is switched in and out
by an unspecified mechanism. The function connecting o and s is the "world
model"; it is the approximation (in the brain) of the actual environmental
physics, f(), that connect o to s through the enviornment.

If f'() is a constant multiplier (like 1.0) then, when the imagination
connection is "switched in" the perceptual signal (p) is a direct result of
the system's output. This is control of imagination: the loop is closed
through nervous system rather than through the environment.

If the nervous system actually constructs an f'() that mimics f(), then f'()
is a "world model"; it is a model of the world that exists between the
efferant outputs and the perceptual inputs of the control system. Once f'()
has been constructed (using Hans' Kalman filtering approach, for example)
then "model based behavior" occurs when the imagination connection is
"switched in" (as before) but now the perception that is controlled is a
result of outputs that have gone through a model of the world "transfer
function" that they would have gone through had the loop been closed through
the environment.

It is important that, in model based control, the outputs go through BOTH
f'() - - to influence p -- and f() -- to influence qi. Of course, since the
system is blind, the effects of outputs on qi are not detected; but the idea
is that the outputs that are controlling the model based perception should
be doing the "right thing" to keep the unperceived qi under "control". That
is, in model based behavior we have:

                    >
                    r
                    v
          p------| |------e
          ^ |
          > >
        > s | <--|f'()|<----| o | System
..................................................
                              > Environment
                              v
   d ---> qi <----|f()|-------|

Note the lack of connection between qi and s. If f'() is a perfect
representation of f() and if d=0 then the outputs that control p will also
give the impression that they are controlling qi. The fact that these outputs
are not controlling qi becomes obvious the instant you let d vary.

Best

Rick