The nature of control

Based upon Bill Powers' and Rick Marken's replies to my previous
posts, it seems to me that we are simply not communicating. Before I
turn to some of the specific points, let me ask a series of general
questions in another attempt to understand your position.

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. Consider a
washing machine. As far as I know, the control circuitry of a washing
machine typically does not use any sensors, yet it causes the motors
and valves to operate in such a way that clothes are cleaned. For the
same reason, a purely central pattern generator can also be a control
system.

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          > > >
Controller | =========> | Plant | =========>
          > > >

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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. Consider the washing machine. By pushing different buttons or
turning different knobs, I can make it wash my clothes in different
ways. Another example of this might be the moth that folds up its
wings when it detects a bat's sonar signal. To me, this like a
nonautonomous dynamical system that switches modes when triggered by a
particular input transition. 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. Also, if the bat continues to
pursue the moth, it does not take any further evasive action in an
attempt to minimize the deviation of its BAT-ATTACK signal from the
desired reference level of zero. It's simply been "wired up" by
evolution to stop flying when it hears a sound of a given frequency.

           ------------- -------------
           > > > >
=========> |Controller | =========> | Plant | =========>
           > > > >
           ------------- -------------

3) Can a nonautonomous dynamical system with noncontrolled feedback
ever by a control system? This one may be a little subtle, so let me
explain what I mean. By noncontrolled feedback, what I mean is that,
though the system receives feedback, it is not the purpose of the
controller to control that feedback (i.e. disturbances in the feedback
are not compensated for). Rather, the purpose of the system is to
control other outputs which are not directly fed back into the
controller. Again, I would say such systems are control systems.
Note that I will grant you that the presence of any feedback
complicates the analysis of the complete system. But this isn't
anything new to neuroscience, since nervous systems have a great deal
of INTERNAL feedback, let alone the EXTERNAL feedback through the
world.

           ------------- -------------
=========> | | | | =========>
           >Controller | =========> | Plant |
      >>==>| | | | ========||
      >> ------------- ------------- ||
      >> >>
      >>==================================================||

4) Finally, we have nonautonomous dynamical systems with controlled
feedback, which I belive all of us would agree are control systems.

What I am trying to argue is that the concept of control is more
general than negative feedback control. It includes other kinds of
feedback (even positive feedback might be involved, such as in the
feeding controllers of the artificial insect and the marine mollusc
_Aplysia_. Positive feedback doesn't result in divergent dynamics
because neurons saturate). My notion of a control system is any
dynamics that can cause some plant to respond in a desired way. A
room full of motors, pipes, etc. won't wash your clothes. But if you
hook them up in the right way and add the appropriate CONTROL (even
w/o any feedback whatsoever!), then you get clean clothes.

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. So I will be very interested to hear your answers to
the above questions.

Both of you seem to place a great deal of significance in the claim
that the only things that matter are the controlled variables,
everything else is just in the eye of the observer, an "irrelevant
side effect". 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. 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).

Now on to some of the specific issues that your replies raised:

First of all, I would like to assure both Bill and Rick that I am not
arguing for the superiority of stimulus-response explanations over
control theory explanations, though I believe that S-R explanations
are sometimes quite appropriate. I would also like to state that I do
not believe that feedback is inherently too slow to be of any
importance in biological systems. Feedback is quite obviously crucial
in many biological systems, but it is not universally necessary.

In claiming that feedback is in continuous operation, I think that you
may be forgetting a very crucial fact about nerve cells. Only action
potentials propagate any significant distance. Any subthreshold
variations in the membrane potential of one cell do not, in general,
affect other cells (there are important exceptions to this, but these
exceptions are not related to my response below). So 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. By the way, I would also like
to point out that action potential propagation is usually one of the
smaller components of delay in the nervous system. 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.

Both Rick and Bill questioned my claims regarding the speed of
feedback in cockroach escape and walking. With the above
observations, let us turn from armchair speculations about how biology
ought to work to the biological data. To keep things simple, I will
just describe Zill's claim that, while sensory feedback is important
at slow speeds of walking in the cockroach, it plays no significant
role at high speeds of walking.

Zill was studying a variety of sensory organs in the cockroach leg.
The roles of these various sensory organs play during cockroach
walking are known. For example, there are groups of organs known as
campaniform sensillae (CS) which are sensitive to stress in the
cuticle along a number of different directions. Different groups of
these organs are known to be involved in initiating and terminating
the stance phase through their connections to a major extensor muscle
in the leg. During slow walking, the bursts in one group of CS (the
proximal CS) immediately precede the burst of activity in the extensor
muscle, while the bursts of another group (the distal CS) immediately
precede the termination. This phasing is not accidental; direct
stimulation of the proximal and distal CS groups have been shown to
produce reflex affects consistent with the functional role described
above.

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.

There is also some more indirect behavioral evidence that sensory
feedback does not play any significant role in fast walking. At slow
speeds of walking, the individual leg movements are quite variable,
while at high speeds, they are very stereotyped. Leg amputation
experiments are also relevant. At slow speeds of walking an amputee
changes its normal leg movements so that that its center of mass is
always supported. However, at high speeds of walking, an amputee
reverts to the normal tripod pattern of leg movements, causing
instability and frequent slipping and falling.

This response is already getting too long, so let me leave most of
your Evolution/Reorganization comments for another time. Let me
respond to just one point. I understand that a biased random walk is
not EQUIVALENT to gradient descent, for exactly the reasons that you
state. My only point was that IF you used gradient information to
bias your random walk, THEN it would be identical to gradient descent.
In fact, your notion of reorganization sounds very much like a search
technique called random search, with a variable mutation rate. We have
been experimenting with a variety of search techniques in addition to
GAs, including gradient descent methods, simulated annealing, and
random search.

In summary, I am not arguing that your notions of closed-loop,
negative feedback control and reorganization are wrong. Quite the
contrary, 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. 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.

Regards,
Randy