(From Bill Powers 940830.1415 MDT)
Hello, Francis --
I'll leave it to you to pass this post along as you see fit.
Real control as I think of it involves a controller acting on the
world in such a way as to essentially _determine_ some aspect of it
My question is: what do you mean by "determine some aspect"? Does this
mean keep the system in a fixed state,
Here is an example of what I mean:
A man picks his shoes out of his closet, puts them on his feet, and ties
the shoelaces. He walks to the front door, maintaining his balance,
reaches one hand out to the doorknob, twists the knob, pulls the door
open causing it to accelerate in angle, then decelerate and stop as he
passes through the opening, and then pulls the door closed hehind him
until he hears it latch. He descends the front steps, walks along the
sidewalk to the garage (avoiding a toy left there by his child), bends
down, twists the garage door handle, pulls the door up and open, goes to
the side of his car, grasps the door handle and pulls the door open,
slides into the driver's seat, adjusts the rear view mirror so the image
of the back window is centered, fishes his key out of his jacket pocket,
puts it in the ignition lock, and twists it until he hears the engine
start. Maintaining pressure on the brake pedal, he moves the gear lever
to the R position, releases the brake, presses the accelerator pedal
slightly, and steers the car backward down the driveway into the street.
He puts the gear lever into Drive, and accelerates the car down the
street, around a curve, and (after pausing at a stop sign) onto the main
road. He accelerates to full speed, avoiding and passing other cars and
keeping his own car in its lane, traveling perhaps 30 kilometers on
several such roads, through traffic, until he arrives at the parking lot
at his place of work, where he aligns the car in an open parking place,
turns the engine off, and gets out.
All these acts of control have occupied perhaps 30 or 40 minutes of the
day. All during the rest of the day this man is engaged in other acts of
control of equal or greater complexity, often consciously controlling
three or four or more variables at the same time, and unconsiously
controlling dozens or even hundreds more. At the end of the day he
reverses the journey, perhaps stopping to pick up a newspaper or
groceries or a tank of gasoline, and arrives at home without ever losing
his way, endangering anyone, or damaging his car. The car ends the day
where it started, very nearly, after an incredible series of highly
improbable, complex, and precise maneuvers to which the man pays
scarcely any attention. And he will repeat this process 200 times a year
without incident.
... or allow the system to wander through a (perhaps infinite) set of
possible states, but such that certain states are excluded? The latter
?would correspond to Ashby's view, who sees control as keeping the s
ystem's variables within a favorable *domain* or range, rather than at
a favorable *point* or state. The little I know about PCT always seems
to use a fixed reference point rather than a reference domain.
The detailed design one would use would depend on the behavior that is
to be explained. A single reference signal with a dead zone in the
control process is equivalent to two reference signals defining upper
and lower limits; it makes little difference, except that in the latter
case two comparators rather than one are needed. If the behavior is one
like keeping a car in its lane in traffic, or steering to a particular
place, or buying a newspaper, I should think that the reference signal
defining the desired state of affairs gives the simplest model. If the
man is just keeping a pencil from rolling off his desk, a one-way
control system will suffice -- all that matters is that the pencil not
go over the edge, and where it ends up on the desk is of little concern.
The particular kind of control model one uses should reproduce the
observed behavior as simply as possible, but as Einstein said, no more
simply.
In the example above, the man's behavior determines the state of himself
and his environment in many detailed ways. To see what kind of control
is involved, one would have to observe (or apply) disturbances tending
to alter the environment, and see how tightly the man maintains the same
condition of the variables being affected by his actions. You could
arrange for a door to stick or for resistance to be applied from the
other side, and see how nearly the trajectory of the door is maintained
in its usual form by variations in the forces that the man applies. You
could put the car in a different place, closer to or further from the
garage door, and see if the place where the man stops reversing it in
the street remains the same. You could have co-conspirators drive cars
near the man on his way to work, to see what distance he maintains from
other cars, how he copes with a slow car in front or someone weaving in
the next lane. By observing videos of the man's performance you could
deduce something about the quality of his control systems, and where he
sets his reference levels for different variables.
The only catch is that you would have to NOTICE all these acts of
control, not simply take them for granted and overlook the myriad
disturbances that would make the outcome different in large and small
ways if the man did not adjust his actions to prevent the effects which
the disturbances would otherwise have.
The difference is less trivial when the state space in which control is
exerted is discrete, or even is continuous but with a discrete set of
reference values. For example, what if my "goal" is to have a roof
above my head during stormy weather? As long as I stay at home, the
control problem is simply to resist any perturbations that may drive me
out of the house. But if some strong perturbation (say a flood or a
hurricane) manages to effectively land me far from my own home, I will
move as quickly as possible to the nearest shelter, independently
whether that is my house or someone else's. The value of the reference
variable (geographical position) at which I now aim may be totally
different from the one I started with. Yet this is still the same
control problem: reaching and maintaining a "favorable" situation.
Well said. Being reasonably sure that you are correctly identifying
controlled variables is not a trivial matter; you can't simply assume
that when you see different people behaving in about the same way, they
are controlling the same variables with respect to the same reference
states. Is a man trying to keep a roof over his head, or stay dry, or
keep his clothes from being wrinkled, or simply coming home in the usual
way and ignoring the rain? Also, will the man stay out in the rain
longer for the sake of having his own roof over his head, or will he
head for the nearest dry shelter? For different people, any one of those
answers might prove correct. You need sustained observation under
varying conditions to rule out wrong guesses (disturbances that aren't
resisted by a change in action). Sometimes you may find a discrete model
the best suited to the phenomenon, sometimes a continuous one. A
discrete model would typically ignore changes in the controlled variable
until they reached a specific state, and then would produce a single act
that opposed the effect of the disturbance. Disturbances that changed
the variable would not result in any behavior unless they caused a
variation past the specific limits. A continuous model would be needed
to account for actions that oppose small effects of disturbances.
Often you find several kinds of control involved in a complex behavior.
Suppose the man looks at the clock, and says "Oh, five o'clock, I have
to get home in time to take my daughter to her party." That is a
discrete decision based on discrete observations and symbol-
manipulation. But the decision "go home" can't be executed as a single
act. It must become the reference condition for many more detailed
control processes, to put the papers on the desk away, get a coat, go to
the car, drive through traffic while comparing progress with the clock
on the dashboard, and so forth. What is named by a decision-making
process as a single simple act can only be carried out by a series of
complex control processes, most of them requiring continuous resistance
to unpredictable disturbances.
This is the sort of consideration that led to the hierarchical control
model, HPCT.
It is again not completely clear to me what you mean by "patterns of
change". Would the above example of a goal state as "being allowed to
move arbitrarily as long as you have a roof over your head" qualify as
a pattern of change?
No, your position in the house would be uncontrolled if the only
reference condition were "keep a roof over my head" or "stay dry" or the
like. Of course it would probably be controlled for other reasons, such
as going to the kitchen for a cup of coffee and so on.
A _controlled_ pattern of change is one that is deliberately maintained
in a specific pattern, like the prancing of a Lippizaner, the movements
of the baton of an orchestra conductor, the movements of a ballet
dancer, or the rising of a bucket in a well as you crank up the
windlass. Controlled patterns of change are identified when motor
actions change in just the way needed to keep the disturbances from
having any effect on the pattern.
I'd rather see it as a static condition. I believe you rather mean
something like a fixed value for a process variable, e.g. keeping speed
at a constant value. Constant speed also means constant change of
position, and thus a dynamic situation.
Yes, that is how I think of it, too. We have perceptual systems that can
represent specific kinds of changes as constant perceptions, the
magnitude of the perception indicating the speed (the speed of rotation
of the second-hand on an analog clock). A constant reference signal
results in a constantly-changing controlled variable, but for the
control system itself, only a constant perceptual signal. The external
observer sees a continuous change, but the control system in question
sees only a static condition. This allows constant reference signals to
be used to specify motion and change or even complex orderings and
sequences. The determination of what is controlled lies in the
perceptual input function.
For example, your goal may be to continuously improve the productivity
of your firm. There is no fixed level of productivity at which the goal
is reached, since competition ensures that a level of productivity w
hich is favorable now will quickly become insufficient once the
competitors have caught up with you.
Interestingly enough, Simon got a Nobel Prize for showing that managers
don't necessarily control in this way! The goal of "more" is inherently
self-defeating in the long run; while it's obviously a possible goal,
not everyone makes this mistake. "Maximizing," aside from involving an
ambiguity of sign in the feedback loop, is an unattainable goal by
definition. It can be done, but control with respect to specific
reference levels works much better: "satisficing." (I think it was Simon
who got that prize -- maybe it was Garfunkel).
In a sense, ever increasing productivity can be viewed as positive
feedback, where the "deviation" from an initial state of low
productivity is amplified. However, it can also be viewed as a second
order negative feedback process: counteract all perturbations that tend
to slow down or reverse productivity increase. What is positive
feedback on the level of the function "productivity" becomes negative
feedback on the level of the derivative function "productivity
increase" (at least if we assume that the reference domain for
productivity increase is bounded downward but not upward).
Positive feedback, or deviation-amplifying feedback as Gary Boyd calls
it, doesn't quite fit this picture. The problem with speaking loosely of
positive feedback is that you forget to take all cases into account. If
the productivity is increasing faster than some reference rate, this
deviation results in a still faster rise, up to the limits of
productivity. But if there is ever a _lessening_ of productivity, the
same positive feedback will reduce the tendency to produce more, which
will reduct the discrepancy even further, which will lead to even less
effort, and so on to the lower limit. The difficulties with positive
feedback can be fully appreciated only by playing with working
simulations, where you can see the consequences of the rule you are
imposing. Positive feedback systems are generally stable only at the
upper and lower limits of output, where no greater (or lesser) action
can physically be produced. They aren't much good for control because
they can't resist disturbances; they simply lock up at one limit or the
other, where they stay until a sufficiently large disturbance flips them
to the opposite state. Postive feedback isn't just a matter of how you
talk about it. It's a matter of the sign of the feedback, and the
amount.
I agree that a second-order explanation using negative feedback works
much better. The second level of control sets the reference level for
rate of increase or decrease, and by taking more of the situation into
account, avoids running the lower systems into their physical limits,
like robots walking with their faces against a wall.
But I would insist that the "goal" of a control system need not be
restricted to a single reference value. All that is necessary is the
capacity to somehow distinguish favorable from unfavorable situations,
and to counteract or eliminate unfavorable ones.
Since the HPCT model consists in principle of as many control systems
operating in parallel at the same level as you like, and as many levels
as you like (up to the highest level needed to explain any actual
behavior), I have to agree with you. When I talk about control, I'm
usually talking about one representative system, but sometimes this
leaves the impression that the model allows only one variable to be
controlled at one level.
The actions required to change an unfavorable situation to a favorable
one will depend on external circumstances. That's the main reason we
need control systems; there's no way to predict what action will be
needed to keep a given variable under control. This holds within the
hierarchy, too: controlling a higher-order variable like "stay dry" may
require moving East on one occasion and West on another, or running to
some other place on one occasion and NOT running on another. The higher
systems vary the lower goals or reference signals as a way of keeping
the higher-level variables under control, and their own reference
signals are in turn varied by still higher systems. And please don't ask
the obvious question; the only possible answers are practical ones which
you can think up as well as I can.
The real problem is that you need to *know* how to counteract
unfavorable situations. In PCT this seems trivial: unfavorable is
defined as "deviating either upwards or downwards from the reference
value". The rule is then simply: if the deviation is upwards, then
counteract by pushing downwards, or vice-versa. In discrete domains,
there are no "upwards" or "downwards" or any other directions. Every
non-favorable state may require a specific counteraction, and this
means that the control system must have a complex knowledge of how to
react.
This can indeed be true, and you would have to construct your model for
such cases accordingly. However, even in discrete domains there are
often indications of "getting better" or "getting worse," and in such
cases the normal control organization is the one of choice. What's
required is that error map in some regular way onto actions that will
work in the direction of correcting the errors. When that's not the
case, good control is going to be very difficult because disturbances
that don't change the situation into a recognizeable error type will not
be resisted. There aren't many situations in the real world in which a
specific action can be counted upon to have a specific result; such
cases as do exist tend to involve someone poking the keys of a computer
keyboard, or the workings of a computer program. Computers are too
damned obedient and reliable; they give the wrong impression of real
life.
This type of control will be much less smooth and easy than the PCT
type, but I still believe it deserves the name "control". As an
example, would you agree to call a game of chess, where the goal is to
create a checkmate (a decidedly non-trivial state), and the
perturbations are the different moves of your opponent, a control
problem?
Yes, I would agree. Even here, however, there are underlying continua,
which both human and artificial players use. "Strength at the center" is
not a discrete variable, nor is the difference between a defensive and
an offensive posture. These analog-type perceptions or assessments play
a part in strategy, although the basic game is based on discrete rules.
Don't forget that even discrete rules can involve quantitative
continuous relationships. There are symbol-manipulation rules other than
logic, you know.
I do think that there is definitely a level of control in which discrete
symbols are manipulated according to symbol-handling rules, and that the
result is true control. In fact, that type of control is described as
level 9 in the current version of my model.
But what if we both try to control the same variable with the same
reference levels? Say we both want to have a friendly conversation or
increase the room temperature. Are we then cooperating?
Possibly, but cooperation in controlling a single variable with respect
to a single reference condition is difficult unless both control systems
are rather laid-back (low loop gain, hence poor control). The problem is
that people don't perceive the same external situation in the same way,
and they don't set their reference levels to the same values even when
they're trying to do so. The better they are at controlling, the smaller
the errors they will detect and try to correct -- and the more difficult
it will be for them to work in parallel with another independent control
system. That's why people usually try to control for different variables
when they're cooperating; one folds the letters and another licks the
stamps while a third stuffs the envelopes. True cooperation on each task
really doesn't work very well. Two blacksmiths controlling the same
hammer will be able to strike twice as hard, but they'll probably hit
the anvil more often than the horseshoe.
Cooperation probably requires the additional condition of coordination
of actions aimed at a common goal.
It works better if the people are controlling independent variables,
each of which _contributes_ to the overall goal. Each person has to be
free to _vary_ his or her actions as disturbances come and go, so as to
keep the controlled variable where it is supposed to be. When you couple
autonomous control systems too closely together, the result is far more
likely to be conflict than cooperation.
···
CC: CSGnet
-----------------------------------------------------------------------
Best,
Bill Powers