Control vcs. noncontrol

[From Bill Powers (920324.1100)]

Chris Malcolm (920323.0830) --

You're not talking about control, Chris, but simple cause and effect.
The only control involved in the scenarios at which you hint is your own
-- you adjust the environment so that what you want to happen happens.

I can think of many examples of this sort of HUMAN control. Say you want
to pour gasoline into a gas tank out of a container that sloshes and
blurps and sends gasoline in all directions. How do you build a device
that will make sure the fuel goes through the little filler hole, no
what its direction of egress from the container? Easy: buy a funnel.

The funnel, however, isn't a control system. If something pushes the
small end of the funnel away from the filler hole, the funnel won't push
back so as to keep the gasoline going through the hole. If it were a
control system, it would.

Real control systems can achieve consistent ends even in real
environments where disturbances can affect consequences of the system's
output, change the characteristics of the environment, and cause changes
in the system's own effector calibrations. If you don't take
unpredictable independent disturbances realistically into account,
you're not designing control systems, but 19th-century automata. I have
no doubt that such automata can be made to do very clever things very
precisely -- as long as they are built so natural disturbances and
changes in their own characteristics are prevented. This is how all
machines were built prior to control systems. Up to a point, it works.
But this is not how organisms work in real environments, and it's not
how any control system to which the name properly applies works.

ยทยทยท

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Pat Williams (920324) -- Such words of appreciation, especially from
you, are high praise indeed. Thank you.
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Randy Beer (920324) --

1) Can a autonomous dynamical system (one w/o any inputs) ever be a
control system? I suspect that your answer would be no (if I'm wrong,
then please tell me). However, I would say that it could.

Then we mean something different by "control system." You aren't the
only one who differs with me on this, but perhaps I can explain my usage
of this term in a way that will make my claim more palatable.

A control system can do something that no conventional device can do:
produce a consistent outcome under conditions where (1) varying actions
are required to produce a consistent outcome, and (b) its effector
calibrations are subject to unpredictable drifts. This is accomplished
through sensing the state of the outcome directly, comparing the result
of sensing with some reference criterion, and using the result of the
comparison to adjust the drive to the effectors. This can result in very
precise control of the outcome, even if the effector sensitivity to the
driving signal varies over a factor of ten and even if there are
external influences that can affect the outcome just as much as the
effector can. What I mean by a control system is a system that can work
this way.

Let's take your Fig. 1, with an addition by me:

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

          > > >
Controller | =========> | Plant | =========> variable
          > > > ^^

------------- ------------- ||
                                                    >>
                      Unpredictable disturbance ====

A controller with or without an input (but without feedback sensing of
the variable) can't maintain the variable at any particular value as
long as the disturbance is present. Neither can it do this if the
plant's response to the signal from the controller varies in amount. In
order for a system like this to achieve stability of the variable
against direct disturbance, the "plant" part must be built so massively
and be so rigidly coupled to the variable that the disturbance simply
has no significant effect.

There's another factor that lies quietly in the background, unspoken.
That is the human manipulator who adjusts this controller and plant so
that (without disturbances) the variable comes to the correct state. The
human manipulator can't do this without sensing the state of the
variable and comparing what is observed with a desired state.

Adjustments of the controller and plant are made until the observed
state of the variable matches the desired state. If the properties of
the controller or plant drift so the variable departs from its desired
state, the human controller will see a difference between the actual and
desired state, and depending on its size and direction, make appropriate
adjustments to plant and controller. So the loop is always closed if
real control exists.

2) Can a nonautonomous dynamical system (one with inputs) that does
not employ any feedback ever be a control system? Again, I would say
yes.

And for the same reasons as before, I would say no. The system you draw
can't counteract disturbances or compensate for changes in its output
properties. The washing machine will happily go through its cycle even
if the waterline is clogged (although some washing machines use feedback
control, and won't proceed until the proper weight of water and clothes
is detected) or the timer sticks on the fill cycle. An open-loop system
can produce a consistent result only if there are no disturbances acting
directly on the result, and only if its output characteristics remain
exactly the same.

I personally find it very strange to talk about this as a negative
feedback system in which the moth's perception of the bat's sound is
controlled. Moth's can hear the bat's sounds for great distances.
Once it begins to fall, this perception doesn't suddenly go away.

I will have to learn more about how these moths actually behave at
different levels of bat sound. If a cockroach can steer by small
differences of odor in an inverse-square odor field (its behavior
strongly affecting those differences), why can't a moth behave so as to
vary the intensity of a bat-sound in an inverse-square sound field? But
I don't want to make a big case of this behavior -- perhaps it works
just as you say it does. I am really more interested in how the moth
works the other 99.9% of the time, when it isn't showing any dramatic
"responses," but is probably controlling a hundred variables
continuously. Why ignore the huge number of control behaviors that are
going on every moment that the moth is active in favor of a few unusual
seemingly open-loop responses?

3) Can a nonautonomous dynamical system with noncontrolled feedback
ever be a control system?

No, once again for the same reason. Consider your diagram, again with
the same addition:
                                                         disturbance
                                                              >>
           ------------- ------------- ||
=========> | | | | =========>variable
           >Controller | =========> | Plant |
      >>==>| | | | ========||
      >> ------------- ------------- ||
      >> >>
      >>==================================================||

I'll agree that with the feedback loop coming directly from the plant,
you now have a system that can be immune to drifts in the
characteristics of the plant and controller, so the output (lower one)
becomes a reliable function of the independent input. In fact, the
sensed state of the plant's output is now compared with the input and
the drive to the controller and plant is automatically varied to keep
the difference near zero. The output of the plant, as sensed, is truly
under control now.

But the variable affected by that output is not under control.
Disturbances that affect the variable will simply add algebraically to
the plant's output and the variable will assume the resultant state. If
there are changes in the link between the plant's output and the
variable, the variable will again change. There will be no action to
bring the variable back to the undisturbed state. So this kind of system
can work only in an unreal or protected environment in which such
disturbances can't happen -- or else if the variable is so tightly
coupled to the plant's output that it can't vary from the state fixed by
that output even when disturbances are present.

Control is not required when a variable affected by a system's output is
never subject to effective disturbance, and when the output effectors
retain perfect calibration. Systems that can work ONLY under such
conditions are not control systems, by my definition.

What I am trying to argue is that the concept of control is more
general than negative feedback control.

I know that the term "control" is used in many circumstances where I
would not use it. I'm trying to promote a more technical usage of this
term, and through this usage a wider understanding of the tremendous
differences between systems with and without negative feedback control.
This isn't terribly important in engineering, where high precision and
massive construction can achieve predictable results without feedback,
and where the main thing is to get the job done. But it is important in
modeling organisms, because organisms have effectors with very sloppy
properties, and the external effects they have on the environment are
subject to all sorts of disturbances that can neither be sensed at their
sources nor predicted. Without the concept of control that I espouse, it
is simply impossible to explain how organisms manage to produce
repeatable consequences in the presence of variable disturbances.

My notion of a control system is any dynamics that can cause some plant
to respond in a desired way.

And if it doesn't quite respond in the "desired" way, what do you do?
You adjust the dynamics. The system will then continue to produce the
desired response until disturbances change or the dynamics of the system
drift. Then you have to adjust it again. To get the system to produce a
consistent response, you have to attend continuously to it, and
substitute your own capacity for negative feedback control for the
capacity you haven't put into the system. That's why, in photographs of
Nineteenth Century machinery, you will often spy the operating engineer
lurking in the background, wrench in hand. Control systems don't need
such babying.

In computer simulations you don't have these problems, because
simulations don't drift and you don't program in random disturbances of
the outcome (unless you're doing control-system models). So the
simulations seem to work just fine. They would not work in a real
environment unless they used negative feedback.

I have talked to some of the people I collaborate with in the systems
engineering department (our collaboration involves the evolution of
control systems using GAs and dynamical neural networks) and they
agreed that they would consider all of the above scenarios to be
control systems.

One of the great disillusionments of my life was the discovery that even
real control engineers don't have a very good grasp of the differences
between control systems and other kinds. To most of them, for example,
it comes as a surprise to realize that control systems control their own
feedback signals, not their outputs. This isn't what they were taught,
but a moment's thought will show that it's true.

I simply cannot understand this position. In the course of controlling
for, say, its velocity, a moth may rip off its wing. This may be
irrelevant to you, but it is certainly not irrelevant to the animal.

You are citing a relevant side effect to refute an observation about
irrelevant side-effects. In your example, an effect of one control
system's action disturbs something else of importance to the organism.
But the importance of the moth's losing the wing is not the same to the
moth as it is to you. To you, the primary effect is that the moth can no
longer fly and will probably starve. To the moth, "flying" and
"starving" are not variables which which it can be concerned. Only the
effects on its internal state of not flying and not eating are important
to it.

In a less trivial example, a cockroach's path to the food patch may
result in the movement of its image across your retina. This is an
irrelevant side effect, because it has no effect on the internal state
of the cockroach. How YOU see the cockroach moving is irrelevant to the
cockroach.

THINGS THAT ARE NOT EXPLICITLY CONTROLLED (in a closed loop, negative
feedback way) MAY STILL BE OF THE UTMOST IMPORTANCE TO THE SURVIVAL OF
AN ANIMAL AND THEREFORE SELECTED FOR (or against, depending upon
whether they increase or decrease the survivability of the animal).

I think you are taking too limited a view of what constitutes negative
feedback. Also, you are not thinking in terms of a hierarchy of control
systems, but only at one level. In a human being, arm position is under
direct negative feedback control. By varying the reference signal for
arm position, however, a higher-level system can cause the arm to reach
out and touch a target -- controlling the distance between fingertip and
target, as seen. And a higher system still could vary the x and y
reference conditions for the relationship between finger and target to
make the finger trace a circle around the target, or a square, or any
other figure -- again, under feedback control. I can't prove it, but I
think that even in natural selection there are feedback control
processes involved, in which the organism's actions control the effects
of selection pressures on the organism, thus effectively controlling the
course of natural selection. You indicate some degree of agreement with
this in your post.

Feedback is quite obviously crucial in many biological systems, but it
is not universally necessary.

Good. I can agree that not every aspect of behavioral mechanisms
involves feedback control. For example, the response of a muscle to a
driving signal does not entail, as far as I know, any feedback that
modifies the driving signal where it enters the muscle. It isn't
necessary even that the larger stretch or tendon reflexes exist, if the
position of an animal's limb reliably depends on the signal entering the
motor neuron: the damped mass-spring properties of the leg might
suffice. However, if it turns out that applying a force to the leg
results in an opposing change in the muscle tensions, then feedback
control is clearly present. Cruse mentions in one article that this is
true of the cockroach. When a clear feedback control effect is observed,
I don't think the use of control theory is optional any more, and S-R
theory is ruled out.

I hope that you would agree that, if some sensory organ does not even
fire an action potential until AFTER the event it's supposed to be
controlling is over, then feedback can play no role.

This isn't true. Ask your consultants about sampled control systems and
z-transforms. In control-system models of neural systems, the variable
of interest is frequency of firing. Also, the physical actions that take
place happen on a very slow time-scale relative to the scale on which a
single impulse is important (particularly when you consider all parallel
pathways that carry the same kind of information around the same
feedback loop). While an action is getting under way, neural frequencies
can change and be changed by the action: there is no such thing as an
"instantaneous" response. All the smoothing that occurs makes neural
control systems continuous on the time-scale that matters.

In considering whether feedback has an effect, you have to consider not
just a single impulse-event, but recurring events. Feedback does not
have to be instantaneous to be effective.

The speed of transmission in chemical synapses, membrane time constants
(which affect the subthreshold responses before an action potential is
fired), and the responses of the sensory structures themselves can all
make significantly larger contributions.

True. But these are the same averaging and smoothing effects that make
frequency, not the single impulse, the measure of choice for neural
systems. The delays of which you speak are not transport lags, but
integration lags. Integration lags have entirely different effects on
closed-loop systems than do pure time-delays.

During fast walking, however, the phase of bursts in the CS shift
significantly relative to the extensor bursts, so that the proximal CS
burst about 20 msec AFTER the beginning of the extensor burst that they
normally initiate (and likewise for the distal CS and the end of the
extensor burst). This fact would seem to make it difficult to argue
that these sensors are playing any role in influencing events that are
over before their influence even begins.

In my attempts at cockroach simulation, I'm using a central pattern
generator similar to yours, with the limit detectors simply triggering
reversals when the leg angle is a little less than it would be if the
pattern generator alone determined the amplitude. At higher frequencies
of walking, presumably the amplitude of leg movement will be less. I
suppose that if it's enough less the limit detectors won't fire until
the central pattern has already reversed.

This is OK with me. I'm not trying to model the pattern generator as a
control system. It's just the output function of a control system (of
several of them), without internal feedback of its own. Just like a
muscle, which works without local feedback. There's always some level of
organization at which you won't find any feedback. When you reach that
level, you're looking at components of a control system, not whole
control systems. You don't have to prove to me that there are
organizational units in organisms that work without feedback control.
All the control systems I design have at least three such units: an
input function, a comparator, and an output function.

On the other hand, the output of the pattern generator for each leg will
provide a reference signal for a leg-position control system, with
feedback from position sensors. This is called for by the data, which
say that a cockroach dragging a weight increases its muscle forces. So
each leg will have a position control system, even though the driving
signals are coming from a pattern generator that inside itself has no
negative feedback control.

Today, by the way, I got a four-neuron pattern generator for one leg to
work so that as a speed signal varies over its range, the speed of
movement slows down, stops, and reverses, the appropriate reset signals
occurring automatically without any need for gated circuit-switching.
The swing phase duration, as per the diagrams in your book, is
independent of the stance phase duration in both directions. Only basic
Beer neurons are used.

I think that negative feedback and plasticity play very important roles
in animal behavior. But I do not believe that they even come close to
exhausting the available mechanisms.

Nor do I believe that the available properties of control systems have
been tapped in the modeling of organisms.

In particular, I think that you underestimate the role of autonomous,
feedforward, and noncontrolled negative feedback dynamics in control. I
also think that you underestimate the role of evolution (and
development, another whole process that intervenes between genotype and
phenotype) in the design of nervous systems.

Well, this will all come down to modeling, won't it?

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Joe Lubin (920323) -- The arm program went into the mailbox quite a few
days ago -- you should receive it any minute. I mailed it the same day
you asked for it.
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Best to all,

Bill P.