Models

CSGnet Archive CSG1997
1

[From Bruce Abbott (970130.1925 EST)]

Rick Marken (970129.0930)

Nevertheless, MCT types will say that the _constant_ settings of
the gain and sign parameters are an implicit model of all these
different environmental functions. There's no stopping them;-)

Quite possibly the use of the term "model" here is a source of confusion.
The parameters of a control system and the environment functions for which
they are suitable are related in the same way that a foot is related to a
shoe that fits the foot. We wouldn't say that the shoe is a "model" of the
foot, yet it does constrain the choice of feet that will "work." And a
plaster cast of the interior of the shoe would in some ways resemble the
feet that fit the shoe.

Regards,

Bruce

2

[Martin Taylor 970224 11:00]

Rick Marken (970221.1240)]

Martin Taylor (970221 12:00) --

>Yes, and I'm almost certain Hans is not at all thinking like that.

Well, here's a chance for you to try looking at actual data for a
change. Try reading [Hans Blom, 970221d] and see if you are still
almost certain that Hans doesn't believe that events in a control
loop occur sequentially.

I have done that, and I see nothing to suggest that Hans believes
events in a control loop occur in the kind of sequence you complained about.
Hans DOES seem to believe that time flows, and that the state of the
control system at time t+dt is quite possibly different from its state
at time t. It is therefore worthwhile noting time as an argument for
each variable. Hans also is clear that the effects of an input at
any point in the loop (i.e. reference or disturbance) are not available
instantaneously elsewhere in the loop--a requirement if the formulae
are to represent any physically realizable control loop. I suspect that
it is this latter point that bothers you. You want the values to propagate
instantaneously around the loop--can't be done in real life, and shouldn't
be done in the mathematics.

That does not mean that things aren't happening simultaneously all around
the loop, the error that we usually see, and the error I don't think Hans
is likely to be making.

Are you asserting that analyzing a control system by sampling its variables
at regular intervals is in some way tantamount to saying that one has to
wait for the effects of some change of reference or disturbance to
propagate around the loop before any new change can be introduced?
Or that it means that one can't compute, say, a new perceptual value
at the same moment one is computing a new output value? Since you
referred me to Hans's message, I have to assume that you mean something
of the kind.

And therefore that you assert that all computational simulations of
control loops are invalid on the grounds that time sample N+1 comes
after time sample N, rather than being simultaneous with it.

OK. I do recall this experiment somewhat, but not the details. I think
I was trying to figure out a way to look at two levels of control
simultaneously. A subject tracked a sinusoidal target; the frequency of
the target was varied. I think I built some models to compare the
tracking accuracy of a single controller (controlling deviation from
the cursor relative to a fixed reference of zero) vs a two level
controller (the higher level system sending a sinusoidal reference to
a the lower order system that was controlling deviation of cursor
perception from varying reference). The two level model did better
than the one level model when the frequency of the track was too
high for the one level model (as long as the reference was an
accurate representation of the target movement).

It wasn't a very high-frequency track, as I remember it, but it would
be better to delve into the archives and find out. What I do remember
was that the predictive time advance of the reference was on the order
of 200 msec, which I computed to be the case, whereas you had assumed
I would claim that the required prediction advance would be on the order
of seconds.

This experiment is a good example of what is wrong with this whole
discussion of model-based control. What's wrong is that people use the
term "model based control" to mean whatever the hell they want it to
mean when they are arguing about whether "model based control" is
involved in behavior. But Hans has described a specific model (which
controls a perception that is generated by a model of the environmental
feedback function -- the model being continuously updated based on the
actual perceptual result of action) that he called a "model-based"
control The "model" in Hans' "model-based" control system is part
of the connection between the reference signal and output variable
in a SINGLE CONTROL LOOP.

Now you (Martin) are calling the two level pursuit tracking model a
model based control model. But that model is nothing like Hans' model
based control model. It is simply a hierarchical control model.

No it isn't. Adding an arbitrary sinusoid to the reference is _exactly_
equivalent to subtracting the same sinusoid from the perceptual signal.
You introduced the sinusoidal reference variation as an act of the God
(you) outside the machine. That's hardly a hierarchic control system.

Nothing about the sinusoidal reference variation is affected
by input from the sensors. It's a one-level control system with an
arbitrary model, a model known _a priori_ to be correct, apart from
being slightly predictive--i.e. affecting the output a little before the
equivalent phase of the disturbance waveform. The exact same model
could equally well have been put into the perceptual input with the
opposite sign.

The
sinusoidal reference input to the lower level system is selected
(by me, the modeller) as a "model" of the target movement. In a real
two level model this reference variation would have to be derived from
the difference between the perceptual and reference input to the higher
level system.

Sure, and then it would be a two-level system, in which the higher level
provided a signal functionally equivalent to the signal provided by the
model in a one-level system--but so far as I know, it hasn't been
demonstrated that the proposed two-level _control_ system would work,
whereas you did show that the one-level system with model does work.

But the main point is that the "modeling" done by this
two level system is not an aspect of the operation of ANY SINGLE
CONTROL SYSTEM that is a part of the hierarchy. The control systems
themselves are simply perceptual control system.

That's right. You (unlike Hans), have not proposed adding any mechanism
for doing the modelling (adaptation). When the control system with a model
is acting, it's _using_ the model; when it's adapting, the model itself
is what the output of some kind of control system acts on. The model
contains (or is) the controlled CEV for one or more control systems of
some complexity, even if Hans's equations don't make it look that way.

So, perhaps I can clarify my objection to "model based control"
models by saying that there is no evidence that any of the _individual_
control systems that make up a living organism operate on the basis of
Hans' (or the MCT) version of model - based control.

With that, I can agree. What I disagree with is your characterization of
what Hans says, and of what your own demonstration shows.

Martin

3

[From Rick Marken (970224.1500)]

Martin Taylor (970224 11:00) --

Hans also is clear that the effects of an input at any point in the
loop (i.e. reference or disturbance) are not available instantaneously > elsewhere in the loop ...I suspect that it is this latter point that
bothers you.

No. What "bothers me" is the idea that events in the loop happen in
sequence. In fact, all variables in a control loop are changing (and
influencing each other) at the same time.

Me:

Now you (Martin) are calling the two level pursuit tracking model a
model based control model. But that model is nothing like Hans'
model based control model. It is simply a hierarchical control model.

Martin:

No it isn't.

Yes it is.

It's a one-level control system with an arbitrary model

Here you are using the term "model" as a synonym for "reference
signal". What you are calling an "arbitrary model" is simply the
sinusoidal reference input to a control system.

You (unlike Hans), have not proposed adding any mechanism for doing
the modelling (adaptation).

Now you are using the term "model" as a synonym for "adaptation". I
can't keep up.

Martin Taylor (970224 12:30)--

Your control simulation _used_ a veriable reference that predicted the >disturbance, using a built-in "internal model."... it [the variable
reference] was the output of a model of the disturbance

And now "model" refers to something that generates the reference input
to a control system.

You have managed to use the term "model" in _three_ different ways (in
only two posts), not one of which is equivalent to the "model" in the
MCT "model-based" control system. Very impressive;-)

Bill Powers (970224.0200 MST) gave some great advice to Bruce Abbott:

The people who catch on to PCT are those who are willing to put aside
all the explanations that others have taken for granted, and really
LOOK at what's going on, without a theoretical point of view blinding
them.

You can do it too. It's (almost;-)) never too late!

Best

Rick

4

[Martin Taylor 970225 10:55]

Rick Marken (970224.1500)]

Sometimes you astound even me with your ability to twist things, and I've
had lots and lots of experience with it. But this message might be the most
extreme example yet. I don't really think there's any point in making a
detailed response, since everything that might be said was said earlier.

But in spite of that, I will make one or two small comments.

Martin Taylor (970224 11:00) --

> Hans also is clear that the effects of an input at any point in the
> loop (i.e. reference or disturbance) are not available instantaneously
> elsewhere in the loop ...I suspect that it is this latter point that
> bothers you.

No. What "bothers me" is the idea that events in the loop happen in
sequence. In fact, all variables in a control loop are changing (and
influencing each other) at the same time.

Yep, as Hans always agrees. As his formulae show. As we have always
dealt with, whether talking about Hans's work or about other simulations
And as you (should) know, we all (I think) agree that this mistake has
been made in the past (e.g. TOTE), and is made by people in other
communities. But not here.

I wonder sometimes whether you actually read the things on which
you comment, or whether you _respond_ only to a _stimulus_ based on the
perception produced by an internal model of the disturbance you think
is likely to be contained in the message.

Me:

> Now you (Martin) are calling the two level pursuit tracking model a
> model based control model. But that model is nothing like Hans'
> model based control model. It is simply a hierarchical control model.

Martin:

> No it isn't.

Yes it is.

> It's a one-level control system with an arbitrary model

Here you are using the term "model" as a synonym for "reference
signal". What you are calling an "arbitrary model" is simply the
sinusoidal reference input to a control system.

No I'm not. I'm using "model" for what _generates_ the sinusoid in
the reference signal. And pointing out that its use in the reference
signal is _exactly_ equivalent to adding its it to the perceptual signal
in a one-loop control system.

I'm very puzzled as to why you can't see that if r = f(t), then (r-p)
= 0-(f(t)+p). Or rather, since I suspect you _can_ see it, why you are
so vehement that it cannot be so.

>You (unlike Hans), have not proposed adding any mechanism for doing
>the modelling (adaptation).

Now you are using the term "model" as a synonym for "adaptation". I
can't keep up.

No I'm not. I'm asking where you got the specification for the model
that generates the sinusoidal reference signal.

Martin Taylor (970224 12:30)--

>Your control simulation _used_ a veriable reference that predicted the
>disturbance, using a built-in "internal model."... it [the variable
> reference] was the output of a model of the disturbance

And now "model" refers to something that generates the reference input
to a control system.

In your case, that's where the model output was used, yes. And that's the
one and only way in which I used "model" in my message.

You have managed to use the term "model" in _three_ different ways (in
only two posts), not one of which is equivalent to the "model" in the
MCT "model-based" control system. Very impressive;-)

Crap:-(

Sorry to show annoyance, but sometimes, really, the things you say are so
extremely silly. It's fun to be silly sometimes--allows one to relax a bit.
But overdoing it is seldom amusing. Sorry again, but there it is.

Martin

···

on CSGnet. And as Hans's message to which you referred me also said.

5

[From Rick Marken (970225.2110 PST)]

Martin Taylor (970225 10:55) to me:

Sometimes you astound even me with your ability to twist things

Thank you. Thank you;-)

I'm very puzzled as to why you can't see that if r = f(t),
then (r-p) = 0-(f(t)+p).

Isn't it (r-p) = (f(t)-p)?

And what's the big deal, anyway? There is no model here. Just a
variable reference signal (f(t)).

Me:

You have managed to use the term "model" in _three_ different
ways (in only two posts), not one of which is equivalent to the
"model" in the MCT "model-based" control system. Very impressive;-)

Martin:

Crap:-(

Why? As I understand it, the "model" in model based control is
a function (call it m(r)) which transforms a command signal (r)
into an output variable (o). An adaptive mechaism (like a Kalman filter)
acts to make the model function, m(), equal the inverse of
the function (call it e(o)) that relates system output (o) to
plant output (x, the controlled variable). The model allows the control
system to "command" outputs (o = m(r)) that bring x to the commanded
value, r. The model function, m(r), doesn't drive
reference values; it drives outputs. There was nothing equivalent
to m(r) in the models to which you were referring. Thus, there was
no nothing equivalent to the "model" in the MCT "model-based"
control system in my models.

Best

Rick

6

[Martin Taylor 970226 14:30]

Rick Marken (970225.2110 PST)]

Martin Taylor (970225 10:55) to me:

Embarrassing typo :frowning:

> I'm very puzzled as to why you can't see that if r = f(t),
> then (r-p) = 0-(f(t)+p).

Isn't it (r-p) = (f(t)-p)?

Yes. Hoist on my own petard. What I meant was (r-p) = 0-(-f(t)+p),
illustrating that it doesn't matter whether f(t) is added to the reference
(as if from a higher control loop) or subtracted from the perception
(as if from a disturbance-simulator model in a single control loop).

And what's the big deal, anyway? There is no model here. Just a
variable reference signal (f(t)).

The variable reference signal comes from somewhere. And it isn't just _any_
variable reference signal; it's a reference signal whose variations
exactly mimic the variations about to occur in the disturbance signal.
There's a model all right--in Bill P's term a simulation--that generates
the variable reference signal that mimics, but precedes, the disturbance.

Me:

You have managed to use the term "model" in _three_ different
ways (in only two posts), not one of which is equivalent to the
"model" in the MCT "model-based" control system. Very impressive;-)

Martin:

Crap:-(

Why? As I understand it, the "model" in model based control ...

I remember referring to a model that generated the predicted sinusoid.
That's the only way I used "model", as I said in the part of my message
that you chose not to quote--the part explaining the "Crap".

I don't remember saying that this model was used in the _same_ way that
the models are used in MCT. Though, on reconsideration, I suppose it
could be. The way your "model" is used, it generates a prediction of
the disturbance. That is compared with the sensed value of the CEV,
either by adding it to the reference or (equivalently) by subtracting
it directly in the perceptual function from the sensed value of the
CEV. The result drives the output function, either way.

I'm not clear how that matters, in the context of the discussion. I was
only repeating what you said you did, three years ago, in the context
of Hans saying that model (simulation) predictions could help. You
showed that they did, in this particular case, bring the control system
model simulation closer to what the human does.

It may gall you that the real-life data that you so often urge people to
look at turns out to seem to support Hans. And I suppose it must be worse
that you generated those data yourself, and it must really bedevil you
that you used words like "predictor" when you originally wrote about it.

But however you feel about it, you did produce those data. There may well
be other explanations for them, but they are consistent with the idea that
a predictive simulation of the disturbance both helps control and makes
the simulated control system with predictor act more like a human than
does one without the predictor.

Martin

7

[From Bill Powers (960824.0900)]
I'm composing this message in Eudora Light's message box and will send it
through
my new Email address, which is

powers_w@frontier.net

All who send me direct mail should make note of this change of address and start
using it now. I will still look in the old address, but not very often.

I would appreciate a brief "hello" message by direct post to test my mailbox
-- say
from Bruce Abbott and Rick Marken. I have a subscription running in parallel
with
the Fort Lewis subscription for the time being. After I'm sure everything works
right I'll switch entirely to the frontier.net subscription and keep Ft.
Lewis only
for people who haven't got the word on the new address yet.

Theres's a lot of work in making the switch -- I have about 140 direct
mail addresses that I have to transfer manually to the "nicknames" file in
Eudora. And there are lots of combinations of ways to type these messages in,
from doing it like this, in Eudora, to using XYwrite (with its nice multiple
windows for cutting and pasting between files)l, to using Notepad. If anyone is
using Eudora on a PC and has any handy tips, I would appreciate them.

This line is a test of the automatic word-wrap in Eudora's editor. Will the
remainder of this line show on your screen without my entering a hard return?

The wrapped part of the line was

this line show on your screen without my entering a hard return?

I know the right margin is too far right, but did the long remainder show up?

Enough for a test message!

Best,

Bill P.
Bill Powers
73 Ridge Place, CR510
Durango, CO 81301-8132
powers_w@frontier.net

8

[From Rick Marken (960826.0810)]

Bruce Abbott (960825.1120 EST) --

why not just use "model" (without the modifier) to mean "model" as
you've always understood it to mean. If anyone wants to refer to the
properties of a system that take account of the properties of the
environment as a kind of model of the environment, they can add the
modifier "implicit." In the context where both are being talked about,
the usual kind of model can be identified as "explicit" if necessary to
preserve clarity, but otherwise this would not be necessary. No babel,
no tower, no confusion.

Since "implicit", like "model", already has an agreed on meaning that
is inconsistent with the meaning you intend when you say "implicit
model", why not use a word that already has the meaning you intend, such
as "not". So we can use the word "model" to mean what we've always
understood it to mean: an analog of something else. And we can use
the term "not a model" or (better, I think) "system parameters" to
refer to those properties of a control system (like its gain and slowing
characteristics) that must depend (if the control system is to control) on
properties of the environment (and on the nature of the perceptual
variable under control, by the way, which is _not_ a property of the
environment) but don't _model_ those characteristics.

Hans Blom (960826) --

It was from him [Pieter Eykhoff] that I learned the close connection
between control systems and models.

I looks like it's going to be real tough for you to unlearn it now;-)

But, I've got to hand it to you, Hans. You do use the word "model"
correctly.

a _model_ M of P is used as a compensator, and its inverse must be
physically realizable:

    u (t) ----------- ----------- y (t)
    ----->|M^-1 (t) |----->| P (t) |----->
          ----------- -----------

Yes, that's what I thought a "model" was.

So Eykhoff's definition of "modern" control theory is that they
contain _explicit_, not implicit models. But the above makes clear
that, implicit or explicit, models play a central role in control
systems.

They play a central role in the control systems that _you_ build. The
question is whether they play ANY role in the controlling done by living
control systems. So far, you have presented _no_ evidence that they play a
any role at all. But lack of evidence has never been much of an obstacle
for the true believer.

Best

Rick

9

[From Rick Marken (960826.1330)]

Me:

Since "implicit", like "model", already has an agreed on meaning that
is inconsistent with the meaning you intend when you say "implicit
model", why not use a word that already has the meaning you intend, such
as "not".

Bruce Abbott (960826.1130 EST) --

I do not mean "implicit" to mean "not."

Martin Taylor (960826 13:30)--

Under what kind of language convention does "implicit" mean "not"?

I guess you guys (including Bruce A. himself) didn't understand what
Bruce A. was saying the way I did. Look again:

why not just use "model" (without the modifier) to mean "model" as
you've always understood it to mean. If anyone wants to refer to the
properties of a system that take account of the properties of the
environment as a kind of model of the environment, they can add the
modifier "implicit."

It looks to me like Bruce is suggesting that we use the word "model" when
we are talking about models (analogs) and that we use the phrase "implicit
model" when talking about "parameters of a system that take account of
properties of the environment" but are _not_ a model (analog) of those
properties. That is, Bruce seemed to be suggesting the use of the term
"model" to mean model and "implicit model" to mean "not a model".

My comments were aimed at pointing out that "implicit" already means
something other than "not" so why not use the word that usually means
"not" -- ie. "not". I know what "implicit" means as, apparently, does Bruce
A. I also know what "model" means and what "control" means. But it seemed
like people were in a frenzy of making up their own correspondences between
symbols and what is symbolized; I figured that Bruce A. was just getting
into the swing of it and using "implicit" to mean "not".

Bruce Abbott (960826.1130 EST) --

let's discuss what I mean rather than the words I use.

It's tough when you use words in ways that are not familiar to me. But
your recent post to Bruce Gregory [Bruce Abbott (960826.1200 EST)] helps
me understand your point a little better, I think. You say:

The wall is _designed_ to serve a _purpose_, the rock is not.

So I think you are saying that the parameters of a control loop are
a "kind of model" (model in the sense of "analog") of the environment
because they are a result of some design (learning, adaptation) process.
I guess I can agree with you as long as we are talking about a particular
"kind of model" -- the kind of model that is _not_ a model;-)

For this reason a control-system's structure and parameters can tell you
something about the environment in which it is designed to function

But my little feedback function experiment shows that a control system's
structure and parameters tell you _precious little_ about the environment in
which it is designed to function . The very same control structure operates
successfully in quite varied environments. Moreover, rather different
structures can operate successfully in the same environment. So a control
structure does not provide much of a model (analog) of the environment.

If your point is that only certain parameters will allow successful control
in certain environments then I agree with you completely! But I think it's
a long (and self-deceptive) way from there to the idea that the parameters
that do allow successful control are _any kind_ of model (analog) of the
environment.

Best

Rick

10

[From Rick Marken (960826.1930)]

Hans Blom (960826) --

     u (t) ----- ----------- ----------- y (t)
     ----->| |----->| inf |----->| P (t) |----->
         + ----- ----------- ----------- |
             ^ - |

···

                                      >

             -----------------------------------------

In this strange (?) case, the process P functions, additionally (!),
as its own model. No separate, explicit model is required! Isn't this
a nice unification between the PCT model and the explicit model
approach?

It's _very nice_ from my perspective since the explicit model approach
evaporates and becomes the PCT approach. The environment, P(t), is the only
model of the environment in a perceptual control system (inf is simply
the output function). But, since P(t) _is_ the environment and not an
analog representation thereof, it seems rather strange to call P(t) a
"model" (implicit or explicit) of the environment. Why not just call it
what it is -- the environment.

Bruce Abbott (960826.1745 EST) --

it is easy to see that I wished to suggest using "model" (without modifier)
to mean "explicit model," the opposite of which is "implicit model," not
"not a model."

But now I am confused again. Are you saying that the parameters of
a control system are an implicit model (analog) of the environmental
feedback function? I thought you agreed that, although control parameters
must be appropriate to the environment, they are certainly not an explicit
or implicit model (analog) of anything in that environment. They are not
an implicit model of the feedback function, for example, because (as I
showed with the feedback function demo) it is not possible to recover the
form of this function even though it is not explicitly expressed in the
parameters of the control system -- because the parameters were constant
while the feedback function was variable.

Only here in Wonderland could what I stated so very clearly be taken to mean
something else entirely.

Yes, Sorry. I thought you had it right. My mistake;-)

But of course, for Humpty, words mean whatever he wants them to mean
(sort of like the way Democrats use "cut" to mean "reducing the amount
of increase," as in "cut your Social Security benefits")

Yes. Sort of the way Republicans use "freedom" to means "the freedom to
do whatever you like to wreck the community (own assault weapons, pay no
taxes, destroy public education) but not to do anything that affects no
other autonomous control system but yourself (don't take drugs-- except
tobacco, don't get an abortion, don't forget to pray in class).

Best

Hubert H. Humpty

11

[From Bruce Abbott (960827.0825 EST)]

Rick Marken (960826.1930) --

But now I am confused again. Are you saying that the parameters of
a control system are an implicit model (analog) of the environmental
feedback function?

Of course not. As Bill P. defined an analog as an _explicit_ model. How
can an implicit model be an explicit model? But it's not important. As I
said before, I don't care what you call it.

But I do have a question for you: is there any difference in your mind
between a model of the environmental feedback function and a model of the
relevant (for the system) aspects of the environment? I thought Hans's MCT
system develops a model of the way the CEV varies, not simply a model of the
feedback function. The former would include the effect on the CEV of both
the system's own actions (via the environmental feedback function) and
regular changes induced by disturbances.

Yes. Sort of the way Republicans use "freedom" to means "the freedom to
do whatever you like to wreck the community (own assault weapons, pay no
taxes, destroy public education) but not to do anything that affects no
other autonomous control system but yourself (don't take drugs-- except
tobacco, don't get an abortion, don't forget to pray in class).

Or the way right-wing extremists are pictured as representitive of the
party. Unfortunately, they seem to be gaining strength, the way the
ultra-left took hold of the Democratic party a few years ago and got the
Democrats kicked out of power. The same will happen to the Republicans,
because most voters are most comfortable walking down the middle of the
road. And then it will be business as usual. I hope you're not counting on
social security to help fund your retirement.

Regards,

Bruce

12

[From Rick Marken (960827.0800)]

Me:

Are you saying that the parameters of a control system are an implicit model
(analog) of the environmental feedback function?

Bruce Abbott (960827.0825 EST) --

Of course not. As Bill P. defined an analog as an _explicit_ model. How
can an implicit model be an explicit model?

No. Bill defined a _model_ as an analog. You suggested calling a model
(analog) an "explicit model". And you suggested calling something else an
"implicit model". Based on your indignant correction of my hypothesis that
the "something else" that your phrase "implicit model" referred to was
"not a model (analog)", I came to the conclusion that what you meant
by "implicit model"was "implicit model (analog)". Now you say it doesn't. So
what does "implicit model" mean?

But I do have a question for you: is there any difference in your mind
between a model of the environmental feedback function and a model of the
relevant (for the system) aspects of the environment?

Sure. They are models (analogs) of different things; one is a model of the
feedback function; the other is a model of whatever "relevant aspects of the
environment" are. In a control system, one relevant aspect of the environment
is the environmental laws (feedback function) relating output to input. So a
model of this relevant aspect of the environment would be identically the
same as a model of the feedback function. Another relevant aspect of the
environment consists of environmental variables that influence the controlled
variable (disturbances). A model of disturbance variables or of the function
relating disturbance variables to the controlled variable would not be the
same as a model of the feedback function.

I thought Hans's MCT system develops a model of the way the CEV varies, not
simply a model of the feedback function. The former would include the
effect on the CEV of both the system's own actions (via the environmental
feedback function) and regular changes induced by disturbances.

Yes. Hans' MCT system is a model of the function relating output to input. If
some of the variance in the input is caused by disturbance variables then
this will affect the form of the model; but Hans' model doesn't try to
determine the components of input variance due to output vs disturbance
variation. Hans model based controller is just given the output and input
variable values continuously and uses the Kalman regresssion method to find
the function ("world model") that relates these variables. When there is no
disturbance variation, the "world model" function will approximate the
feedback function; when there is disturbance variation, the "world model"
will approximate the Republican view of reality -- mixed-up confusion;-)

Or the way right-wing extremists are pictured as representitive of the
party. Unfortunately, they seem to be gaining strength, the way the
ultra-left took hold of the Democratic party a few years ago and got the
Democrats kicked out of power.

I'll take a left-wing over a right-wing extremist anyday!

Best

Rick

13

[From Bruce Abbott (960827.1055 EST)]

Rick Marken (960827.0800) --

Bruce Abbott (960827.0825 EST)

Of course not. As Bill P. defined an analog as an _explicit_ model. How
can an implicit model be an explicit model?

No. Bill defined a _model_ as an analog.

Bill defined what _I_ (and others) call an explicit model an analog. I
suggested that we could forgo the "analog" and just use "model" when we mean
"analog" or "explicit model." Round and round and round we go. Who cares?
In the future I will use "model" to mean "analog" and "structure and
parameters tuned as required by environmental characteristics" instead of
"implicit model," if that will make you happy. Then perhaps we can get back
to discussing the properties of control systems insteady of endlessly
pursuing this stupid digression.

But I do have a question for you: is there any difference in your mind
between a model of the environmental feedback function and a model of the
relevant (for the system) aspects of the environment?

Sure. They are models (analogs) of different things; one is a model of the
feedback function; the other is a model of whatever "relevant aspects of the
environment" are. In a control system, one relevant aspect of the environment
is the environmental laws (feedback function) relating output to input. So a
model of this relevant aspect of the environment would be identically the
same as a model of the feedback function. Another relevant aspect of the
environment consists of environmental variables that influence the controlled
variable (disturbances). A model of disturbance variables or of the function
relating disturbance variables to the controlled variable would not be the
same as a model of the feedback function.

Then why do you insist on suggesting that I am trying to link "implicit
model" to the environmental feedback function, period? A properly-tuned
system would have to take account of the normal effects of disturbance on
the CEV, not so?

I'll take a left-wing over a right-wing extremist anyday!

I'll bet you would. I'll take someone capable of thinking _rationally_
about the issues over either one.

Still waiting for you to describe how all those "wonderful models" of
reorganization of which you spoke work -- you know, the ones that make any
"knowledge" of the environment unnecessary. (:->

Regards,

Bruce