Quasi Homeostasis: multiplier feedback

CSGnet Archive CSG1993
1

Hello. I found this in the Newsletter of the America Society for
Cybernetics from March '93. Comments welcome.

Quasi Homeostasis, Aha!

by Faisal L. Kadri, Ph.D.
PO Box 1082
Sarina ON N7T 7K2
Canada

It might come as a surprise to some to know that regulation can be achieved
by processes other than negative feedback. Here, I would like to
re-introduce an alternateive regulator. The familiar negative feedback
control system uses a subtractor as the error producing element; the
alternative regulator uses a multiplier instead (fig. 1). I call the
process "quasi homeostasis". Mathematically, the concept is not new. When
written in equation form, the basic system can be described by an intergral
equation called "the Fredholm equation of the second type".

        _ ______
  x / \ zx | |
------| o |---->| A |--------->
       \_/ |______| |
        ^ |
        > ______ |
      z | | | |
        --------| H |<----
                >______|

Fig. 1, block diagram

The basic quasi homeostatic system is made of a fast responding feedthrough
element A and a slower feedback element H, both of which can be nonlinear.
The way the system workds can best be illustrated with an impulse-like
stimulus. It is easy to see that for a nontrivial respose, system H must
have a static constant term which corresponds to feedthrough gain at
initial conditions and a gain of opposite sign to cause the feedthrough
gain to reach a temporary near-zero value.

My Aha! experience came after a simulation program shows quasi homeostasis
to closely resemble the animal behavior processes of deprivation followed
by satiation, and I am encouraged to look for real life systems where the
alternative regulator offers a better, closer likeness. So if you have a
problem for quasi homeostasis, or if you wish to know more about it, then I
will be happy to hear from you.

O----------------------------------------------------------------------------->

Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .

2

From Tom Bourbon (930519.0940)

Cliff Joslyn (18 May 1993 17:51:41)

I am not sure I follow Kadri's reasoning, or his use of words. Or perhaps
the problems come from what he said, as filtered through your abstracting
of highlights. In either case, the lack of understanding is on my side.

Can you clarify a few things for me?

Hello. I found this in the Newsletter of the America Society for
Cybernetics from March '93. Comments welcome.

Quasi Homeostasis, Aha!

by Faisal L. Kadri, Ph.D.
PO Box 1082
Sarina ON N7T 7K2
Canada

It might come as a surprise to some to know that regulation can be achieved
by processes other than negative feedback.

He is saying there are possibilities other than negative feedback, isn't he?
(Like Rick, in his post in reply to yours, I would be surprised were that
the case, but that is my problem. I just want to be certain Kadri says
that.)

Here, I would like to
re-introduce an alternateive regulator. The familiar negative feedback
control system uses a subtractor as the error producing element; the
alternative regulator uses a multiplier instead (fig. 1). I call the
process "quasi homeostasis". ...

       _ ______
x / \ zx | |
------| o |---->| A |---------> (TB: Is this "output?")
      \_/ |______| | (Is x the "stimulus?")
       ^ |
       > ______ |
     z | | | |
       --------| H |<----
               >______|

Fig. 1, block diagram

The basic quasi homeostatic system is made of a fast responding feedthrough
element A and a slower feedback element H, both of which can be nonlinear.

Is the "feedthrough element" an input-output transfer function?

Does he acknowledge that neg. fb. systems also accommodate nonlinearities?

The way the system workds can best be illustrated with an impulse-like
stimulus.

The multiplier must be in "o".

What is this system supposed to control -- its output ? To match its input,
which is characterized as a "stimulus?"

If his model is a replacement for a negative feedback control system, which
is best illustrated controlling continuously in a (potentially) continuously
disturbed environment, why it (his model) best illustrated with an
"impulse-like stimulus?"

It is easy to see that for a nontrivial respose, system H must
have a static constant term which corresponds to feedthrough gain at
initial conditions and a gain of opposite sign to cause the feedthrough
gain to reach a temporary near-zero value.

Is he saying that H must have gain equal in magnitude and opposite in sign
to "feedthrough gain?" Is input multiplied by the negative of output:

               input * (-1 * output)
or is it by:

            input * (-1 * (ft gain * output)) ?

My Aha! experience came after a simulation program shows quasi homeostasis
to closely resemble the animal behavior processes of deprivation followed
by satiation, ...

Did he examine or discuss what a negative feedback control system does when
it reaches a state of high-magnitude error (as in a state of deprivation),
then is allowed to act? (Did he describe what animals do?) How does the
behavior of his model compare to that of a nfb control system under those
conditions?

... and I am encouraged to look for real life systems where the
alternative regulator offers a better, closer likeness.

Better and closer than ... ?
Likeness to ... ?

I will appreciate any clarification of my foggy impressions.
Until later,
  Tom Bourbon

3

>From Tom Bourbon (930519.0940)

>Cliff Joslyn (18 May 1993 17:51:41)

I am not sure I follow Kadri's reasoning, or his use of words. Or perhaps
the problems come from what he said, as filtered through your abstracting
of highlights. In either case, the lack of understanding is on my

side.

With one small exception (below), everything I wrote was exactly
everything he wrote. This is all I have. I was hoping it would make
sense to you people!

He is saying there are possibilities other than negative feedback, isn't he?
(Like Rick, in his post in reply to yours, I would be surprised were that
the case, but that is my problem. I just want to be certain Kadri says
that.)

Yes. Basically, I interpret him as saying "do it just like negative
feedback, except replace subtraction w/multiplication". If that makes
sense. Does it?

> _ ______
> x / \ zx | |
>------| o |---->| A |---------> (TB: Is this "output?")
> \_/ |______| | (Is x the "stimulus?")
> ^ |
> > ______ |
> z | | | |
> --------| H |<----
> >______|

The one exception from above is that he labeled the edge coming in
from the left as input, and that leaving on the right as output. I
presume that `o' is the multiplier, taking x and z as inputs, and
producing zx as output.

Is the "feedthrough element" an input-output transfer function?

Got me.

Does he acknowledge that neg. fb. systems also accommodate

nonlinearities?

He doesn't deny it.

Beyond this, I have no further clarification or explanation.

Perhaps someone on this list could solicit a broader explanation from
him?

O----------------------------------------------------------------------------->

Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .