"disturbances"; conflict

[Martin Taylor 950920 17:30]

Hans Blom, 950912d

A conceptual problem: disturbances. In my vision, disturbances do
not exist in the real world. The world has its properties, some
known, some unknown. We focus on some and disregard others. What
we call "disturbances" are those properties of the world that we
cannot model or do not want to model.

A conceptual problem, indeed. Also, I think, one of word usage. That
word "properties" is the sticker, here. If the fact that someone else
has bought the last ice-cream bar, which I wanted, is a "property" of the
world, then I have to agree with you. But I'd prefer to use the word
"property" of the world more in reference to the way the world behaves
when acted upon rather than the momentary factual state of the world.

I realize that the two blend together, and that the world does in fact
behave differently if that last ice-cream bar has been sold than if there
is one left. But that blending is across time-scales, and across levels
of control. Of course, if you don't think in terms of a hierarchy of
scalar control systems, you can't make a clear distinction. But I think
that you can, if you treat only scalar control systems.

To me it makes sense, thinking of a scalar control system, to think of a
"property" of the world as relating to the feedback function between the
output "port" and the CEV. It affects how the output influences the CEV.
A "disturbance," on the other hand, is an influence on the CEV that is
independent of the output of the control system. It does seem conceptually
helpful to keep the two notions apart.

Since in a hierarchy lower-level ECUs are part of the feedback path of
higher-level ones, they contribute to the "properties" of the world. But
they slow things down. Disturbances to lower ECUs are shielded by the
actions of those lower ECUs from affecting the higher ECUs to the same
extent. But at the same time (if the lower ECUs are non-linear) those
disturbances also change the properties of the feedback functions of the
higher ECUs, and that's where the blending between "properties" and
"disturbances" comes in.

If you look at the whole hierarchy, or at a complex single control unit,
then the distinction between "property" and "disturbance" becomes fuzzy
and it becomes fair to say:

What
we call "disturbances" are those properties of the world that we
cannot model or do not want to model.

But looking at a single SCALAR control unit, which we can do anywhere in
a hierarchy, there is a useful distinction to be made.

ยทยทยท

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

Returning to conflict and the "orthogonality" of CEVs, Bill Powers made a
very good comment about the "degree" of conflict being representable as
the cosine of the angle between controlled CEVs (though, Bill, there was
no need to talk about a "multidimensional equivalent of 90 degrees" since
the two CEV directions define a single plane). If two CEVs are near parallel,
but not actually parallel, they do define a sufficient basis space to avoid
conflict, in the sense that both can have arbitrary reference values
satisfied, but being near parallel, their mutual influence will generate
feedback loops that might have positive components. The magnitude of
the mutual feedback loop is (I think) the product of the two gains times
the cosine of the angle between them. If I'm right, then although there
is a static solution to the conflict resolution, that solution will be
dynamically unstable unless G1*G2*cos(theta)< +1.

My introduction of the concept of an output-defined environmental variable
(ODEV) suggests another potential problem with conflict. For any control
system operating in a multidimensional environment, the ODEV has some
direction which must correlate with the direction of the CCEV (the cosine
of the angle between ODEV and CCEV must be non-zero--the side-effects are
contained in the sine of that angle). Now consider the following picture,
which represents two CEVs, in different control systems:

         >CEV1
         >
   ------|-------CEV2
         >
         >

These control systems SHOULD not be in conflict, since they are orthogonal.
But now suppose that each has only one mechanism for affecting the CEV,
as follows:

ODEV1\ |CEV1 ODEV2\
      \ | \
       \ | \
        \| -----\-----CEV2
         \ \
         >\ \
         > \ \

Individually, each can control effectively, but together, they cannot.
They act through mechanisms so related that each effect of one output
exactly parallels the effect of the other output, which is (I think) what
Hans Blom was getting at in his discussion of conflict (Hans Blom, 950907e).

So we actually have two places where conflict can occur, and I suspect that
it is both the angle between the CEVs and the angle between the ODEVs that
matter.

In PCT, it is usually assumed that control can be accomplished through
a variety of mechanisms, which is not the situation described above. Variety
of mechanisms corresponds to the possible existence of many ODEV directions
for any particular CCEV, though at any moment only one ODEV direction is
active. If that direction results in ODEV conflict, the action of lower
level control systems will probably shift it to some degree--other mechanisms
will be used to achieve the perceptual control. ODEV conflict, therefore,
will in most cases be a resolvable dynamic conflict, not an irresolvable
(static) conflict or an irresolvable (expanding) dynamic conflict.

(Parenthetically, note that what happens with two parallel ODEVs is a
reduction of the output degrees of freedom. If the mechanisms cannot be
changed, the two CEVs can be controlled only through time multiplexing.)

Martin