[From Bill Powers (950919.0530 MDT)]

Jeff Vancouver (950918.1710) --

I think it is dangerous to lump all dynamic equilibruim process as

either control processes, as Bill P. _seems_ to be doing,

It is even more dangerous to base opinions on a hasty reading of the

literature. As other members of this net will attest, I have spent

considerable time discussing the difference between a simple equilibrium

process, in which there is no power amplification, and a control

process, which is defined by very narrow and specific properties. There

are many dynamic equilibrium processes that are not control processes.

But some processes that have been _interpreted_ in terms of dynamic

equilibrium are actually explainable only as control processes.

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What I am not clear about is where biology, etc. generally stand on

this issue. I was under the impression the homeostatic processes

and set points were an accepted concept (although each must be

empirically demonstrated). Is this not the case?

Many biologists, enough to have been inconvenient for control theorists,

reject any concept of a set point. They prefer to see homeostasis as a

passive dynamic equilibrium process, of the same nature as a weight

stretching a spring. As Bruce Abbott has said, they often specifically

reject a control-system model, and then proceed to describe a process

that can ONLY be explained as control. You'll have to ask a biologist

why.

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Hans Blom (950919)--

Bill, I have had the time to analyze the problem now.

OK, you have solved it. I thought it would have to be something like

that.

Bill, how would your program handle different values of b, say from

0.1 to 10.0 and from -0.1 to -10.0? Mine would need no changes and

it would show the same high performance in all cases. Indeed, b

could be a time function in my program and the performance would

still remain identical.

As you can recall from looking at my previous post, the RMS errors I was

getting were 5.582. I get exactly the same error for k = 1, 10, 100, -1,

-10, and -100. Remember, I have disabled the "randomize" statement so

the random generator always starts with the same seed. This is handy for

comparing runs.

# My program is

k := 100.0; {or whatever value you like}

{RUN THE MODEL MAXTABLE + 1 TIMES}

for i := 0 to maxtable do

begin

x := k * u + d[i]; { ENVIRONMENT}

b := 1/k; { ASSUMED ADAPTATION}

u := u + b * (r[i] - x); { CONTROL SYSTEM }

sum := sum + sqr(r[i] - x); { ACCUMULATE FOR RMS CALCULATION}

end;

{==============================================================}

So this raises the question that has been bugging me since the beginning

of this interchange: why does your model work? It's easy to see why it

works in one sense: the calculations are designed to make the error

exactly zero. You can explain that the output is being adjusted to

nearly cancel the disturbance. All this I understand.

However, your model works nearly as well when you _don't_ calculate the

right disturbance. Leave out your new division by b, and make the

disturbance calculation simply dnew := x - u, without the b multiplying

u. For positive values of k, the RMS error will still be only a tiny

fraction of the amplitude of the disturbance. For your b = 1.0 in the

environment equation, the error is 1.9. for b := 0.2 the error is 3.7.

You would still need an adaptation to compensate for the sign of b, but

that's a separate question.

Obviously, the disturbance is not being calculated correctly for k = 0.2

(dnew is theoretically only 1/5 of the required size), yet the error is

still only 0.004 of the peak disturbance. In fact what you find is that

dnew is very different from the actual disturbance -- just enough

different and in the right direction to maintain control!

What I suspect, but can't prove, is that your method is simply a

limiting case of a general control method basically identical to mine.

Perhaps while I'm gone you can give some thought to this.

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That's really all -- off to the airport.

Best to all,

Bill P.