[Hans Blom, 970924b]
(Rick Marken (970923.1240))
Science is, indeed, an actual example of model based control.
So it exists! Hurrah! And that coming from you! Quite unexpected...
What then remains to be established is when and where it occurs, not
whether ;-).
The model based control process that is science is something that
can be done (as far as I know) by only one kind of organism --
humans.
But then this disappoints me terribly. It sounds awfully humano-
centric. What's so special about humans that only they would be able
to do this "high level" stuff? The one percent genes that makes us
different from chimps?
And, indeed, it seems that it can be done by only a subset of humans
at that.
And this surprises even more. What to call it? Scientocentric? I
propose that it exists in a lot of places, but hard to recognize --
obviously: _you_ don't ;-). Science is, after all, a mere
formalization and systematization of what humans (and higher
animals?) do anyway, at all times in our normal "daily life".
Let's go back to basics. What is model-based control? It is the
scientific theory to explain why control can remain of high quality
even though the characteristics of the environment may change
dramatically. And the practice of how to construct such systems, I
must add, as an engineer.
Regrettably, I must stick to the very basics. The most explicit
diagram of a model-based control system is:
r ----- e ------- a
---->|+ |------>| C |-->--
-->|- | ------- |
p> ----- ^ |
> ---|--- |
>------------->| WM |<----
> ------- | controller
> > ----------
> ------- | world
------<--------| W +|-----
···
+|<---- d
-------
where C is the controller, p its perception, r its reference and a
its action. W is the world it lives in (in control engineering
parlance "the plant" or "the system to be controlled"). All that is
in the PCT model as well. What is extra is the block WM (for "world
model") which contains a mechanism to adjust C (through the link
between WM and C) based on some type of cross-correlation between a
and p. What is actually "modelled" in WM can vary. If WM constructs
p = f (a)
then f is called the plant's "forward model". Read the symbol "=" as
"a good fit for"; no _exact_ identity is required, as practice shows,
for control quality to be good). If WM constructs
a = g (p)
then g is called the plant's "backward model". Other models are
possible as well, such as
h (p, a) = 0
which gives no _explicit_ expression for either p or a. All of these
models are -- in a sense -- identical: they capture the regularities
that exist in the relationship between p and a in some function,
which has a finite/limited number of parameters. Only the forward
model's parameters (those of the function f) can be in a one-to-one
relationship with the parameters of the world W. But there is nothing
that restricts us to the forward model: if the backward model is more
useful, construct _it_. The mathematical operations to be performed
in WM are the same: it's always cross-correlation.
There is nothing that forces us to consider WM to be a "world model":
that is just an interpretation. Call it CT, for "controller tuner",
and you are correct as well. There is also nothing that forces WM to
be a separate block. Combine it with C and you have an "adaptive
controller" with the following block diagram:
r ----- e ------- a
---->|+ |------>| |-->--
-->|- | | C | |
p> ----- p | | a |
>------------->| |<----
> ------- | controller
> > ----------
> ------- | world
------<--------| W +|-----
> +|<---- d
-------
What is different from the standard PCT diagram? The basic difference
is that the controller C has two additional inputs: p and a. In other
words, it "knows" what it perceives (p, not just the error e) and how
it acts (a). Other than that, C is just a different (more complex and
generally time-varying) function.
Are those differences important? Yes. Without access to p and a no
adaptation/learning is possible (in this theory! there may be others
where this is not required, although I doubt it). And no. Since even
the PCT controller generates a, it has direct access to it; so why
not use it? And since even the PCT controller has access to r and e,
it could easily reconstruct p from p = r - e.
But note that in the second diagram no "world model" is visible
anymore. It is only by noticing the correspondence between both
diagrams that we can "perceive" that the second diagram "contains"
one.
(If you were actually doing model based control, Hans, you would
revise your model based on evidence; since you don't do this, I have
to conclude that your own model based control model does not apply
to you; open loop control seems more likely;-))
What's the difference between "model based control" and "open loop
control"? If in an "open loop" _control_ (according to your
definition?) still is (appears?) possible, then it must logically be
"model based control", I guess. I can make no other sense of what you
say here; in PCT, the notion "open loop control" is an oxymoron,
isn't it?
Greetings,
Hans