[Hans Blom, 930927]
(Tom Bourbon [930902.0900])
Finally I had some time to analyze your third "revised diagram", the one
that you say contains adaptation. It does. Let me try to find its place
in the taxonomy of control engineering. The important part of the dia-
gram is:
PCT MODEL OF PERSON B
r = A-[/\/\/\]=0
! r=[if q > Q, dk = rand dk]
! \!/
! !!!!!!!!!!!!!
! ! i ! c ! o !
! !!!!!!!!!!!!!
\!/ /!\ !
present !!!!!!! ! !
value !!>! C !!!! !
of = p !!!!!!! e=p-r !
A-/\/\ ! \!/ !
!!!!!!! !!!!!!! dk
! I ! ! O !<!!!!
!!!!!!! !!!!!!!
/!\ !
In the adaptor loop, q = present sum (integral) of the error signal, e;
dk = random change added to k (in O). B has become an adaptive
controller. In the runs I did, now a couple of years ago, B converged
within a few seconds on a value for k that kept A-/\/\/\ near zero, and
A kept c-t=0. ...
Now some of the differences between this particular adaptive PCT model,
and the model described by Hans seen even clearer to me. For one
thing, the equivalent of what Hans called the "second controller" in
the adaptive controller has no model for A and there is no expectation
of what A will do; rather, the "second loop" has a reference signal for
the value of the time integral of sensed error being < a criterion
value, and an output function that adds a random change to the
integration factor of the primary control loop. There is no "optimal"
value of anything -- any k that keeps the integral of sensed error
below the criterion value will "stick." For this loop, anything that
is "in the ballpark" is good enough.
First, let me redraw the adaptive part of your diagram into an equi-
valent one:
---- -----------
r | | | |
-->|+ | e | |
p | |---->| gain |--->
-->|- | | | (k) |
> > > > >
---- | -----------
···
/|\ dk
> -----------
>-->| gain |
> control |
-----------
Isolating this part shows that it can be categorized as belonging to the
class of what are called "automatic volume control" (AVC) circuits.
Don't take AVC too literally; other functions, such as "automatic fre-
quency control" (AFC) are implemented similarly. The goal is, each time,
to keep a certain variable (here: e) at a certain level or, in your
case, within certain bounds. In principle, AVC is a type of feedforward
control, that often results in a more or less logarithmic transfer
function, very similar to that of our sense organs -- the eye's bright-
ness control and the ear's loudness control allow tremendous dynamic
ranges of brightness and loudness to be processed accurately. But your
scheme works only because it is part of a larger feedback loop, where
the output of the gain block is manipulated in such a way that the
difference between r and p is (on average) larger than a minimum and
smaller than a maximum.
AVC and AFC are used in radio receivers, TVs, tape recorders and a great
deal of similar signal processing equipment, as well as in some control-
lers. AVC keeps internal signal levels and/or the audio output at such
values that the signal is not so large that it becomes clipped -- with
all the distortion that this implies -- nor so small that it drowns in
noise. AVC can be called an adaptive system, still so simple that it is
easy to explain its function.
The internals of the "gain control" block have not been specified yet.
They depend upon the required overall function. Here, you want to mani-
pulate B's loop gain in such a way that r-p stays within limits. This
can be done through some function that couples the integral of the error
with the gain. Bill Powers suggested that you use a random coli-type
function. Your initial idea was more straightforward and probably both
faster and more robust. Did you compare the performance of both
adaptation methods?
Now some of your remarks:
the equivalent of what Hans called the "second controller" in
the adaptive controller has no model for A and there is no expectation
of what A will do ...
There MUST be an expectation. Without some kind of expectation that can
be manipulated, no control is possible. In this case, the expectation is
that A will act in such a way, that perception p will, on average, stay
within well-defined bounds. That seems to be all you need. It might seem
that you do not need to know A's perceptions in order to establish his
input-to-output transfer function. Yet you have some idea of what A
perceives, although not in all details: that is because you manipulate
A's perceptions. Implicitly, therefore -- and in a very clever way, I
must say -- you establish a relation between what A sees and what he
does.
rather, the "second loop" has a reference signal for
the value of the time integral of sensed error
The "sensed error" is the indication how well the expectation is met. If
not, the adaptation works in such a way that it eventually WILL be met.
Is this again a problem of semantics? A model of A is an approximation
of A which contains only the things of interest; all else is left out. A
model need not accurately predict A's moment to moment actions; a gener-
al impression of one facet of A's actions might suffice, as is the case
here.
There is no "optimal"
value of anything -- any k that keeps the integral of sensed error
below the criterion value will "stick." For this loop, anything that
is "in the ballpark" is good enough.
This goes back to earlier discussions in which I said that Bill Powers'
notion of a reference level is too specific in many cases. Sometimes all
you need is that a value remain within an upper and a lower limit, and
not necessarily that it remains fixed -- as good as possible -- at a
certain value. In your case, "optimal" translates into "in the ball-
park". For some reason, the latter was optimal for you (in terms of
design effort?).
Now some of the differences between this particular adaptive PCT model,
and the model described by Hans seen even clearer to me.
Let me show you why I think that there are no fundamental differences
between a PCT model and a "standard control engineering model", if I may
call the thing so. Let us start with the classical PCT-diagram.
r
+ \|/
- -------
---------->| C |-----------
> p ------- e \|/
------- -------
I | | O |
------- -------
/|\ ------- | qo
-----------| W |<----------
-------
W stands for "the world", everything outside the organism. Rearrange,
lumping C and O, into a more engineering-like diagram:
---------------------------------
> >
> ----- p ----- ----- |
-->| I |--->|- | qo | | |
----- r | CO|------>| W |->--
------------>|+ | | |
----- -----
Put an identical I-box in the path of r. If I is one-to-one, this is
allowed. Neither physically, physiologically, psychologically, mathe-
matically nor philosophically this seems disallowed. In practice, it has
the great advantage of putting r' onto the same scale as the observable
p'. Only in this (observable) sense is it meaningful to talk about or
design tests for a "controlled variable".
---------------------------------
>p' |
> ----- p ----- ----- |
-->| I |--->|- | qo | | |
r' ----- r | CO|------>| W |->--
--->| I |--->|+ | | |
----- ----- -----
Now merge both I's with the CO-box.
---------------------------------
>p' |
> ----- ----- |
----------->|- | qo | | |
r' |ICO|------>| W |->--
------------>|+ | | |
----- -----
The ICO-box now represents the organism, with the exception of r (or
r'), which must be put inside. So a better representation would be:
---------------------------------
>p' |
> ----- ----- |
> > > qo | | |
----------->|ICO|------>| W |->--
>(r)| | |
----- -----
The latter two schemes are notations used in engineering. In particular,
the last scheme -- with its internal r -- is used under those conditions
where r itself is or may be a function of p'.
The latter two schemes do not necessarily denote single-input/single-
output (SISO) systems. Think of all lines as vectors (multiple measure-
ments/actions outside, nerve bundels inside), and you have a MIMO (mult-
iple-input/muliple-output) system.
One detail that I keep having a difference of opinion about with Bill
Powers is whether there is a "direct" path from "action" to "percept-
ion":
r
+ \|/
- -------
---------->| C |-----------
> p ------- e \|/
------- -------
I | | O |
------- -------
/|\ /|\ | |
> ------------------------- |
> ------- |
-------------| W |<------------
-------
But this, too, may be a matter of semantics: where is the border between
"inside" and "outside"? Is my skin inside or outside? How about the
tissues between muscle fibers and skin? When I act AS IF I catch a ball,
my actions are hard to distinguish from those actually employed when I
play ball. So it seems that no physical outside is required in order to
have a functional feedback system. It is easy to add an internal "gener-
al model" (correlator + memory + adaptation mechanism), such as the one
that I propose must exist, to the last diagram:
r
+ \|/
- -------
---------->| C |-----------
> p ------- e \|/
> ------- |
>--------->| M |<---------|
------- ------- -------
I | |--------->| O |
------- adjust -------
/|\ /|\ | |
> ------------------------- |
> ------- |
-------------| W |<------------
-------
This is only slightly more complex than the scheme that you employed,
isn't it? The machinery inside M is hardly more complex than the one you
propose. Just one additional line in the diagram...
Greetings,
Hans
