Control Theory: a guided tour.

[From Bill Powers (2007.11.08.0714 MST)]

I finally got my copy of "Control Theory: a guided tour" by J. R. Leigh (1992). I can't remember who recommended it -- was it Fred Nickols? I agree that it's very clearly written.

I'm writing because Chapter 12, State Estimation, discusses the Kalman Filter, and I want to know what Richard Kennaway (and anyone else) thinks of it. It reminds me a lot of the way we construct models and adjust them so their behavior fits that of a real person. This is apparently taken as the primary means of control. It works this way:

A control output u is sent into "the plant" (the real environment) and also into a model of the plant. The output of the real plant (or a vector of outputs) is compared with the output of of the model, and discrepancies are corrected by adjusting the parameters of the model. When the discrepancies have been minimized, the response of the model to the control output u is nearly the same as the observed respose of the real plant to the same output, so the output of the model can then be used as a pseudo-perception of the output of the plant. The output of the model is then compared with the desired state of the output of the plant (i.e., the reference signal that we use in PCT), and the error signal is u, the control output that enters the real plant as well as the model. Thinking of the model as a perceptual input function, then, we can see that the whole system works just like a PCT control system in the imagination mode. The main difference from real closed-loop control is that this system can't resist changes in the perception due to unmodelled variations in the environment, such as novel disturbances or changes in properties of the plant that are not monitored. The control system works in the imagination mode, taking the reference signal being sent to lower systems directly as one input, and producing an imagined output that is like the real plant's output. The actual output of the plant is monitored, but only for the purpose of adjusting the model -- not as a real-time feedback signal to the comparator.

The entire modeling step seems superfluous to me, since the result of the modeling, after all adjustments are complete, is a perceptual signal that is just like the perceptual signal obtained by observing the output of the plant. Why not just use the measured output of the plant, which is what we want to control, as the perceptual signal? The only advantage I can see of using the model is that if perception of the real plant's output is interrupted for a brief time, the model will keep running and providing an artificial feedback signal, so the control system can continue producing a reasonable control output for some short time. This was discussed some years ago in CSGnet exchanges with Oded Maler. To obtain this advantage, however, one must give up the ability to resist unpredictable disturbances in real time, and greatly reduce the bandwidth of control (because of the need for continuous correction of the model parameters and smoothing of random disturbances, which are ignored in the model).

It could be that this model-based control process might work satisfactorily for higher-level systems that are slow anyway, and that are somewhat protected against disturbances by the actions of lower-level systems. I would have to see some experimental evidence, however, before I would believe that any brain process works that way.

I'd like to say something about this in the new book, but am uncertain of my ground. Any help will be appreciated.

Best,

Bill P.

···

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[From Richard Kennaway (2007.11.08.1705 GMT)]

[From Bill Powers (2007.11.08.0714 MST)]

I finally got my copy of "Control Theory: a guided tour" by J. R. Leigh (1992). I can't remember who recommended it -- was it Fred Nickols? I agree that it's very clearly written.

It was me, actually. I'll take a look, although it would be great if a Real Control Engineer that works with this sort of stuff could say something. The same goes for the appendix I'm writing for Bill's current book. I'm sure it would be improved by a critical and knowledgeable eye.

···

--
Richard Kennaway, jrk@cmp.uea.ac.uk, http://www.cmp.uea.ac.uk/~jrk/
School of Computing Sciences,
University of East Anglia, Norwich NR4 7TJ, U.K.

[From Richard Kennaway
(2007.11.08.1705 GMT)]

[From Bill Powers
(2007.11.08.0714 MST)]

I finally got my copy of “Control Theory: a guided tour” by J.
R. Leigh (1992). I can’t remember who recommended it – was it Fred
Nickols? I agree that it’s very clearly written.

It was me, actually. I’ll take a look, although it would be great
if a Real Control Engineer that works with this sort of stuff could say
something. The same goes for the appendix I’m writing for Bill’s
current book. I’m sure it would be improved by a critical and
knowledgeable eye.

Richard Kennaway, jrk@cmp.uea.ac.uk,

http://www.cmp.uea.ac.uk/~jrk/

School of Computing Sciences,

University of East Anglia, Norwich NR4 7TJ, U.K.
Hi, Richard –
You should be getting a CC of a post to Dr. Paul Beatty of the U. of
Manchester, which will explain itself. I’m cc-ing this to him so he can
see what goes on in our world, and I’m taking the liberty of including
your post that I’m replying to.
It’s my impression, from the Leigh book [Paul: “Control Theory: a
guided tour”], that control engineers have been as much confined as
aided by their mathematical approaches. That’s only an impression, but
one reason I’ve been lax about learning all that stuff is that it seems
to be hostile to an intuitive grasp of how control works, and how control
processes might be organized. The idea that control systems control input
information never appears, though it’s an obvious one to me. Or maybe the
problem is that control engineers, with full access to all parts of
artificial control systems, have never had to consider what it would be
like to BE a control system. Their concept of feedback, for example,
never seems to include the requirement that it give the control system a
perception of the external variable under control: they feel free to add
stabilizing or predictive embellishments to the feedback signal that
destroy its role as a report about the external world, and even to the
reference signal, destroying its role as a specification of what is
desired. The engineer designing the system gets the result he wants, but
the control system then loses its resemblance to a living
system.
One thing I’ve noticed is what seems an overemphasis on, or perhaps some
confusion about, predictive control. I’m sure predictive control works,
but I’m also sure that other ways work much better when they can be used.
Somehow the prediction of the output never seems to include a prediction
of what the output is going to be with the predictive part of the
system taken into account
. The prediction always seems to be a
prediction of what the state of the controlled variable will be if the
control system doesn’t change what it’s doing – but of course it
will change what it’s doing, so the prediction will be wrong. Or
else what they are calling prediction is nothing of the sort. Does that
make any sense to you?

Best.

Bill

···

At 05:05 PM 11/8/2007 +0000, you wrote:

[Martin Taylor 2007.11.11.23.57]
(Almost finished with Remembrance Day, so I may forget what I'm posting :slight_smile:

[From Bill Powers (2007.11.08.0714 MST)]

I finally got my copy of "Control Theory: a guided tour" by J. R. Leigh (1992). I can't remember who recommended it -- was it Fred Nickols? I agree that it's very clearly written.

I'm writing because Chapter 12, State Estimation, discusses the Kalman Filter, and I want to know what Richard Kennaway (and anyone else) thinks of it. It reminds me a lot of the way we construct models and adjust them so their behavior fits that of a real person. This is apparently taken as the primary means of control. It works this way:

A control output u is sent into "the plant" (the real environment) and also into a model of the plant. The output of the real plant (or a vector of outputs) is compared with the output of of the model, and discrepancies are corrected by adjusting the parameters of the model. When the discrepancies have been minimized, the response of the model to the control output u is nearly the same as the observed respose of the real plant to the same output, so the output of the model can then be used as a pseudo-perception of the output of the plant. ...
The entire modeling step seems superfluous to me, since the result of the modeling, after all adjustments are complete, is a perceptual signal that is just like the perceptual signal obtained by observing the output of the plant. Why not just use the measured output of the plant, which is what we want to control, as the perceptual signal?

What you are describing sounds to me like a planning system. You model the world and act on it in imagination, which is much faster and less dangerous than trying out actions with irrevocable effects in the real world. In the modelled world you can call back the action and try a different one. Subjectively, we (or I) seem to do it all the time. We aren't always right about the effects of a modelled action when we use it in the real world, but we are right often enough (or near enough) to be useful, and we are usually right enough that we avoid fatally catastrophic actions (or at least we are wrong on that only once in a lifetime).

The modelled world is obviously not capable of introducing unexpected disturbances, but it is possible to imagine the perceptions that might arise if this or that externally generated event were to occur, and to imagine the possible results of actions we might employ to control against them.

There would be no point in that kind of modelling in a world with linear, or even monotonic, feedback functions. But the real world is of that kind only at the lowest levels.

Martin

[From Rick Marken (2007.11.12.1120)]

It's my impression, from the Leigh book [Paul: "Control Theory: a guided
tour"], that control engineers have been as much confined as aided by their
mathematical approaches. That's only an impression, but one reason I've been
lax about learning all that stuff is that it seems to be hostile to an
intuitive grasp of how control works, and how control processes might be
organized. The idea that control systems control input information never
appears, though it's an obvious one to me.

My impression is similar. I have described what I think are the
problems of applying engineering (which is often purely mathematical)
control theory to an understanding of living systems in my review of
"Control theory for humans":

http://www.mindreadings.com/BookReview.htm

Fell free to send the reference to Leigh.

I believe that engineering (mathematical) control theory can be as big
an impediment to understanding control in living organisms as
conventional economics can be to understanding the collective control
that we call an economy.

Best

Rick

···

On Nov 9, 2007 10:16 PM, Bill Powers <powers_w@frontier.net> wrote:

--
Richard S. Marken PhD
rsmarken@gmail.com