[From Bill Powers (920814.1000)]
Dennis Delprato (920813) --
When you break your silence you do it in great style. That is an outline
for an important paper. I hope you're going to write it.
Here's some more scaffolding for the article (partly continuing the
conversation with Oded Maler (920814)). This is part of an outline for
something I'm writing, but feel free to use any part of it that seems
useful. The following will benefit greatly from some running examples, but
I leave them out here for brevity. It contains some experimental usages
that may make things clearer -- "disturbances" in particular.
···
-----------------------------------------------------------------------
First, break behavior down into actions and outcomes. Most behaviors are
named by the outcomes: peeling an apple, toasting some bread, driving to
work, splitting some kindling, and so on. The actions that bring about
these outcomes aren't normally mentioned.
It's possible to use outcome-names for behaviors because outcomes repeat,
even in a variable environment. It's necessary to use outcome-names because
outcomes are far more regular than the actions that bring them about. If we
described all behaviors in terms of their action components, there would be
almost no regularity to name.
Outcomes are affected by an organism's actions and by independent variables
that also affect the outcomes. The only way the outcomes can remain regular
is for the actions to vary in opposition to the effects of the independent
variables, or disturbances.
There are two main kinds of explanation for how actions might be adjusted
to achieve the observed regularity of outcomes. One explanation involves
compensation. The other involves control. Both require that the organism
sense its environment.
The compensation answer requires that the organism sense the states of
independent variables that can influence the outcome. This answer has
several drawbacks. First, all the causes of disturbances of the outcome
must be known; if they are not, compensation isn't possible. Second, the
effect of all independent variables on the outcome must be known; that is,
when these variables change it's necessary to calculate the effect of the
change on the outcome. Third, the action used to counteract the disturbance
comes from a different source than the disturbance. So the effect of the
action on the outcome must also be known and separately calculated so as to
have the right opposing influence on the outcome; in general, the path by
which the action affects the outcome is different from the path by which an
independent variable disturbs the outcome. Fourth, the links to the outcome
from both action and independent variable must have constant properties. If
those properties change, to the same extent the calculations will be in
error and the outcome will fail to be stabilized. Fifth, the calibration of
the sensors and actuators must remain constant.
The control answer requires only that the organism sense the outcome
itself. It does not have to sense the independent variables causing
disturbances of the outcome. This answer has the drawback, at least for
discrete actions and outcomes, that some disturbance must be allowed in
order to serve as the basis for the action that prevents further
disturbance. However, control will work when the independent variables
can't be directly sensed, or when they can't be sensed accurately, or when
they vary unpredictably on the same time-scale on which actions take place.
Control will also continue to work accurately over large changes in output
calibration. Thus control is the more general answer to the question of how
consequences are made repeatable in a variable environment.
In some cases both compensation and control can be used. Compensation --
reacting directly to an independent variable capable of disturbing an
outcome -- can produce an immediate action that is approximately right for
opposing the disturbance. If the remaining disturbance is small enough, a
control process based on sensing the outcome itself can succeed in removing
the rest of it, achieving exact stabilization of the outcome without any
protracted period of error. This combination works best for discrete
variables. For continuous variables, for example those involved in
balancing upright, compensation does not add any appreciable improvement in
performance.
Compensation and control work at about the same speed. Both require sensory
computing processes. Both require computation of outputs. A control
process, however, is always faster and simpler when any complexity of
calculation of output is involved. In a control process the required output
is derived continuously from the sensory information, often by a simple
subtraction, and varies as the sensed outcome varies. Compensation,
however, requires continuous calculation of properties of the environment
and the body, which even for simple behaviors can entail calculations of
impractical complexity (as in computing the inverse dynamics of an arm in
order to move it). Furthermore, the negative feedback involved in control
allows high amplification of responses to disturbances, increasing the
bandwidth of responses greatly over that obtainable with a compensatory
system. In general, a control process is faster than an equivalent
compensatory process. And of course, a control process is, in the steady
state, far more accurate than a compensatory process, not relying on the
environment always having exactly the same properties, not relying on
unchanging calibrations of sensors or actuators, and not requiring that the
independent variables responsible for variations in the outcome be known at
all.
----------------------------------------------------------------------
Best,
Bill P.