Something (was: simulation and calculation)

[From Oded Maler (970128)]

Re: Bill P.

I took the discrete-time model just to simplify presentation. I
dislike integrals and they look ugly in ASCII. It is assumed that dt
is small enough to approximate the physical world. In fact, one of my
current research directions is to study controllers whose sampling
rate is slower than 1/dt (or that their computation time is larger
than dt, etc.). For simplification reasons I also took reference
r=[0,0,..,0], this is not a crucial issue.

For the meaning of feed-back, I, of course, dont't object to your
anthrpocentric use of the term (feed-back is how the environment
reacts to our actions and influences), but bear in mind that control
people use "feed-back control" as designating the controller I/O
function.

Re: Richard R.

I think (but may be wrong) that there is some confusion concerning
"control" versus "calculation" and you are ignoring a middle possibility.
Let us consider two extremes:

1) AI-planning-calculation: to catch a ball, you look once, then close
your eyes and every other input channels, abd execute a precomputed plan.

This is completely unreasonable in dynamical environment, and nobody
claims it to be the picture.

2) PCTish, modelless behavior (is the control of you know what..):
By some reorganizational miracle you have some servo hierarchy
that can bring perceptions to references. There is no mathematical
relationship between the input-output function of the controller
and the dynamical laws that govern the environment.

I think this is too extreme even for you. You admit that in order for
a controller to function it needs to be of a certain form. It needs to
apply forces that go well with the dynamics of the environment. It has
to "know" that moving the mouse usually moves the cursor in the same
direction. Clearly our arms do not solve differntial or linear
algebraic equations consciously.

The MCT approach to the production of intended results is based on
open-loop concepts of behavior that were (unfortunately) borrowed by
control theorists (who had been moving in the correct direction until
then) from psychologists.

I am not sure your perception is true. All mathematical control theory
is about closed-loops. If you have a model of the environemnt it does
not mean that you have to close your eyes and ignore disturbances.

But I have to go.

--Oded