prediction; math -Reply

[Hans Blom, 960116]

(Bill Powers (960116.0500 MST))

One point comes up, however, that I would like to raise some
questions about.

... and that I would like to clarify.

Hans Blom's model-based control system, at least in the versions I
have seen, does not "predict" the state of the environment. It
models it, but what it models, if it is working right, is the
_current_ state of the environment, not a future state.

last observation was NOW, it certainly can model the future state of
the environment. Although I didn't do that in my demo, the capability
is there. And it is used in some types of optimizing control as well,
for instance where you want to minimize the expected control error
over the whole future, from now until infinity, or over some future
period of time, say from now until the end of your life.

Remember that my controller was able to remain in control when no
observations were forthcoming (under the condition that the world did
not change in the mean time)? That is the equivalent thing. Speed the
prediction up and what you do is predicting the future.

Why would a controller want this possibility? I think that one reason
is to be able to keep controlling some modalities while the attention
(the employment of the perceptual apparatus, e.g. the direction in
which one looks) is focussed on something else. In other words: to
realize parallel processing cq. parallel control.

What other use of the prediction capability? For planning.

What we want is for the perceptual signal NOW to match the reference
signal NOW, and for the effects of actions to counteract
disturbances that are acting NOW.

Not only. By greatly speeding up, beyond real-time, the process of
prediction we can compute (model) what will happen in the future
given a prespecified future course of action. By testing a number of
possible courses of action, a search for optimum action is possible.
(This is a "forward" way of finding optimum behavior which avoids
reverse models). All this again under the condition that the world
doesn't change appreciably in the mean time.

Wouldn't it be nice to know the effect of your actions before you
attempt something? That is what an internal world-model makes

Not always, of course. You can accurately precompute the amount of
your savings account given the way you save. But then your bank can
go bust. Oops, forgot to model that...