A brief introduction to Perceptual Control Theory
William T. Powers
Perceptual control theory, or PCT, is a theory of human and animal
behavior. It is based on the principles of control theory and was
originally inspired by the work of the early cyberneticists (Wiener and
Ashby, primarily). Its history goes back to 1953.
Other theories about behavior have been based primarily on two concepts:
reaction to external events and circumstances such as stimuli and
reinforcements, and generation of actions by cognitive plans or
computations. PCT fits into the space between these approaches, because
it is about a kind of behavior that has features of both of them. This
kind of behavior is called _controlling_.
Controlling
While most people have an idea of what "controlling" means, it's mostly
an informal idea and the word is used to refer to many different
processes. We talk about the "controls" of an airplane, but they don't
control anything unless someone operates them. A "control" experiment
doesn't actively control anything; it's simply a comparison experiment.
The "controller" (or comptroller) of a company doesn't control the
company; he or she manages the bookkeeping. And a "control" spirit that
a spiritualist invokes is still something else.
There's no point in arguing about what a mere word "really means." Even
in a scientific approach we have to use words, but to avoid all the
confusions of usage we simply ASSIGN a meaning to the most important
terms. In physics, "work" doesn't mean working up a sweat; it means
force times distance and nothing else. In PCT we do the same thing:
control has one and only one meaning, and it is never used to refer to
anything else. There are various ways to state this meaning, but here is
a useful one:
A is said to control B if, for every disturbing influence acting on B, A
generates an action that tends strongly to counteract the effect of the
disturbing influence on B.
This isn't the whole definition, but it's a basic part of it. It's
important to understand from the start that this definition doesn't fit
many of the common usages of the term. For example, it is said in
chemistry that temperature controls the rate of a chemical reaction. But
that doesn't fit the definition: if some independent influence tends to
change the rate of the reaction (stirring the mixture, for example), the
temperature will NOT change so as to counteract the effects of the
disturbance on the reaction rate. So whatever effect the temperature
has, it does not "control" the reaction rate in the PCT sense. It may
influence or affect the reaction rate, but no PCTer would say that it
controls the reaction rate.
On the other hand, there are many usages that would fit the definition.
We say, commonly, that a driver controls the path of a car by steering
it. Does this fit the definition? If something tends to disturb the path
of the car, like a crosswind, will the driver produce an action that
opposes the effect of the crosswind on the path of the car? Definitely
yes. This is a true example of control as we use the term in PCT.
Theories of Behavior
There's another aspect of controlling that isn't covered by speaking
only about resistance to disturbances, the definition given above. The
driver of a car doesn't just resist the effects of crosswinds and bumps
to keep the car going in the right direction. The driver also determines
what the "right direction" is. If a crosswind is blowing from the right,
the driver might be maintaining a constant steering pressure _to_ the
right, keeping the wind from making the car drift off the road. But at
any time, we might observe the driver turning the wheel so the car goes
clear out of its lane, crosses the oncoming traffic lane, and turns onto
a cross street. If that crosswind keeps blowing, the driver might turn
the wheel a little less or a little more than would be normal to
negotiate the turn, so the resistance to disturbances still continues.
But now there is _extra_ action, the amount needed to make the car go
around the turn.
Where does this extra action come from? Before we start developing the
PCT explanation, let's pause to look at how the traditional theories of
behavior might explain it. Say we see the car going along in a straight
line for a while, and then we see it turn left at a street marked
Lincoln Street. What made the driver turn left at Lincoln Street?
First, let's consider the theory that behavior is caused by external
events that act on the nervous system to cause muscle responses. An
operant-conditioning theory, for example, would say that the street sign
with its label "Lincoln Street" serves as a discriminative stimulus. The
driver turns down Lincoln Street because in the past, doing so has led
to consequences that were reinforcing. Each time the driver happened to
see the sign for Lincoln Street and turned left into it, something
happened that increased the likelihood that the same turn would be made
the next time the same disciminative stimulus appeared -- the next time
the driver saw the street sign saying "Lincoln Street." Maybe the
driver's girl-friend lives on Lincoln Street. Of course there are other
reinforcers and other discriminative stimuli, so the driver wouldn't
_always_ turn down Lincoln Street, but if that did happen, the
explanation would be the one just given.
What's wrong with this theory? The main thing is that it doesn't explain
how this can happen. The crosswind may or may not be blowing, so the
"left-turn-response" that makes the car turn the corner on one day might
make it climb the curb on another day, when the crosswind is different.
Obviously, when the crosswind is blowing from the right, turning the
corner requires a different physical action on the steering wheel from
what it requires when the crosswind is blowing from the left, or not
blowing at all. So somehow that discriminative stimulus (which is the
same every time) has to produce a _different_ response, according to
what the wind is doing. And it has to be just the right kind of
differentness, because getting the car around the corner calls for an
exact amount of steering effort, not just "turning the wheel." Steering
is a _quantitative_ process, not just a matter of generating a response
that's in the right category.
There are other problems with this theory, but that will do for now.
Now what about the other main kind of theory, the one that says behavior
is produced by cognitive plans or computations? One of the main
practical problems with this kind of theory is that it requires a
staggering amount of knowledge on the part of the driver's brain. The
driver who intends to turn at Lincoln Street must know the speed of the
car, its mass and moment of inertia, the condition of its tires and the
road, the physical laws governing moving masses, and the properties of
the muscles and the steering linkage that will convert neural commands
into physical results. Using this knowledge, the driver must reason
backward from the desired result of making the turn to deduce the neural
signals required to produce just the desired effect. In technical terms,
the driver's brain must compute the inverse kinematics and dynamics of
the physical system that the neural signals will affect, solving
multiple nonlinear differential equations for just the signals and
signal patterns needed. And then, of course, exactly those signals and
signal patterns must be generated and sent to the muscles.
On top of that, there's that pesky crosswind. A driver in a closed car
has no way of sensing the crosswind. Seeing a piece of paper blowing
across the road doesn't provide enough information to compute the amount
of extra neural output needed to compensate for the effects of the wind
on the car. So there is really no way to compute the amount of
compensation needed to counteract this disturbance. To solve that
problem, we must add even more complexity to the processes in the brain,
bringing in adaptive Kalman filters and other such arcana. Such problems
only give mathematicians a healthy appetite, but engineers would quail
before them. The brain is a wonderful computer, but it's not a
_precision_ computing device, and the equipment it works through is not
very precise, either. The engineer who must actually make this thing
work is handed a bushel basket of $4.95 calculators, and is told to
solve 20-dimensional nonlinear differential equations with them.
That just can't be how it works.
So both of the major explanations of this simple behavior, and all other
behaviors, have severe difficulties when you get down to the level of
how such behaviors would actually be carried out. The problems are in
the basic architectures being proposed, the basic underlying scheme that
must accomodate the details. When we get into the details, we see that
impossible feats are being demanded.
The control system architecture
There is a kind of system, a control system, that can accomplish the
apparently impossible in a relatively simple way. It can steer the car
around the corner even if an unpredictable crosswind is blowing, or if
there's a soft tire, or if the road is a little slippery, or if the
steering linkage has become sloppy. It can do this if the muscles are
fresh or fatigued, or even if the nerves driving the muscles become a
little tired or lose a few of their connections to the muscles. It can
do it even if traffic has forced the driver into the wrong lane, so the
path of the car has to swing wider than usual.
The hallmark of a control system is that it can create reproducible ends
by variable means. As a matter of fact, that's just how William James,
100 years ago, described living organisms. Living organisms don't
produce repeatable actions. They produce repeatable _results_.
If you think of behavior as being a matter of simple cause and effect,
it is very hard to see how any system could reliably produce a given
end-result if the processes that lead to that result are unpredictably
variable. If you usually stand in a particular place to open the
refrigerator door, how can you open it if there's something in the way
and you have to reach from a different place with a different bodily
orientation? If a door normally opens with a certain amount of push, how
can you open it if it sticks and requires more force to open it? If your
right front tire goes flat, how can you keep steering the car straight
when you don't even know the tire is flat?
If you pay close attention to the most ordinary actions, you'll realize
that something is always a little different each time you do them.
Either you're starting from different initial conditions, or the
environment has changed a bit, and sometimes a lot. Why aren't you
always missing things when you reach for them, or bumping into furniture
and open doors, or sitting down on thin air because somebody moved your
chair two feet? A Greek philosopher said that you can't step into the
same river twice; what he meant is that the world may be repeatable when
you take the big view of it, but the details are always changing. And
when we actually do things, we're always running into those changing
details.
How can any behaving system manage to keep producing the same results
again and again, in a world that won't sit still? If the other theories
offered any explanation (they generally ignore this problem), it could
only be that you have to learn how to handle each new variation by trial
and error, or by revising calculations. But a control system doesn't
have to do that for each little variation. It can tolerate very large
variations in the environment, including large disturbances that would
change the outcomes of action by a lot if they weren't counteracted. Of
course control systems, like all physical systems, have limitations, but
the limitations are far less restrictive than they are for either of the
other two kinds of proposed organizations.
The theory of control systems, in fact, shows us how a relatively simple
system can manage to produce reliable and repeatable results in an
environment that has a large component of unpredictability -- in other
words, in the real world.
How controlling works
If you start with the idea that a behaving system controls outcomes or
results rather than the actions that produce them, you can invent
control theory from scratch. The first thing you realize is that this
can't be done just by creating reproducible actions. The same action
will have different results depending on what's going on in the
environment. What you want is some basically simple way to produce a
given result that doesn't depend on being able to predict exactly what
action will be needed to produce it.
So ask yourself how you do it. Here you are, driving along in your car,
trying to keep it on the road in a gusty crosswind. You don't know when
the next gust is going to come, and you don't know exactly how much
traction your tires have on the road. If fact, if you start thinking too
much about such things, your attention is going to wander and so is the
car. So what DO you do? You watch the outcome that you're trying to
control.
In the windshield you see the road and probably part of the car. This is
what you watch. When the road looks a certain way in relation to the
car, you know you're in your lane. What you want, of course, is to keep
the scene in the windshield looking that way -- that's the result you
want to accomplish by your steering efforts. If the scene shifts, you
have to do something to bring it back to the right appearance. You have
to adjust your steering efforts to the right or left. If the picture of
the road moves to the right of the correct position relative to the car,
you turn the steering wheel a little to the right. The road shifts
toward the right place (or the image of the car shifts toward the right
place on the road, it makes no difference how you think of this), and
you reduce your steering effort, until finally everything is just right
again and your steering efforts stop changing. I hope you were able to
keep up with those alternating uses of "right."
It's not hard to figure out how steering effort should change as the
scene in the windshield changes. If you see yourself too far to the
right, your steering effort changes toward the left. The farther to the
right you are, the greater the change in the steering effort to the
left. Just the opposite relationship holds if the car is too far to the
left; the steering effort changes toward the right, by an amount that
depends on how far left the car appears to be. So there is one simple
rule involved: whichever way the car is seen to be deviated relative to
the road, the steering effort must change in the opposite direction.
There's only one small issue remaining: where is the "right position" on
the road? If you look carefully at the road as it appears in the
windshield, you won't see any "right position." You will see where the
car actually is relative to the road, but that's all. There's nothing
out there to mark the right position.
If there's nothing out there to mark the right position, the right
position must be defined In Here. In your head. Somehow, you have a
picture in your head of how the scene in the windshield will look when
the car is in its lane. And you compare this "reference condition" in
your head with the actual scene that you see in the windshield, to see
whether the car is left or right of, or exactly at, the reference
condition. Whatever difference there is tells you which way to turn the
wheel, and by how much.
And there you have it, with a few details to clean up: a control system.
Anyone could have invented it. In fact a lot of people have invented
this kind of system, the first recorded instance being in about 240 BC.
It was reinvented repeatedly for the next 2000 years, but unfortunately
nobody saw the general principles involved. Those weren't worked out
until the 1930s. Now it all seems obvious, except to those who haven't
yet caught on to what the engineers of the 1930s accomplished, or who
stubbornly want to go on thinking the way people thought before then.
The basic control system
To make this theory useful we have to generalized it to cover all
possible examples. Control can involve any sensory input, not just
vision. It can involve any variable aspect of the sensed world, not just
position. And while it always involves the use of muscles, the way the
muscles act on the world is widely varied. Let's put together a simple
block diagram that can be used for any example of behavior.
Perceiving
The first thing we need is a way to sense the result that is to be
controlled, the "controlled variable." This implies some sort of sensor
that can detect the state of the controlled variable and represent it as
a signal inside the controlling system. We don't need to go into detail
here; some controlled variables are very simple, like the brightness of
a light, and some involve complex aspects of the environment, like your
position in the stock market. We can put off the details for future
study just by designating a controlled variable in the environment, a
box that contains all the machinery needed to sense it, and a signal
coming out of that box, representing the current state of the controlled
variable. We'll call this box the "perceptual input function," and the
signal that comes out of it the perceptual signal.
The perceptual signal isn't just an on-off signal, indicating that
something is there or not there. The controlled variable does just what
the name says: it varies. If the position of the car in its lane is the
controlled variable, or at least the variable we hope to control, then
that position can vary from far to the left to far to the right,
continuously. As it varies, the perceptual signal representing it
varies. We don't need to say exactly how it varies; it's sufficient to
say that its variations represent variations in the controlled variable
(of course until we have the "controlled" variable under actual control,
it's just a variable).
Comparing
That takes care of modeling the system's knowledge of where the car is
in its lane. Now how do we model where the car _should be_ in its lane?
The first control system engineers puzzled over this for, perhaps, a
couple of years before they saw the obvious answer. The reference
condition has to be indicated by a second signal.
We naturally call this second signal that defines the reference
condition the "reference signal." The clever solution that the engineers
saw was this: if the perceptual signal can vary over some range, then
one of its values in this range would represent the desired state of the
controlled variable that's being sensed. If a second signal were
supplied, just like the perceptual signal but arbitrarily adjustable to
any particular value, then it would represent the reference condition of
the perceptual signal -- and therefore of the controlled variable.
And most important, if we could somehow _compare_ the values of these
two signals, the difference between them would would indicate by its
sign which way the discrepancy went, and by its magnitude how big the
discrepancy was. Since the engineers were working with electronic
systems, they devised a simple electronic circuit that received the
perceptual and reference signals, and put out an electrical signal
proportional to the difference, positive or negative according to the
sign of the difference. In the nervous system, the same function is
easily constructed using excitatory and inhibitory neural connections.
The reference signal now represents that sense of how the road _should_
look in the windshield, and the perceptual signal represents how it
_does_ look. The comparison function or comparator we have just built
shows how you could (not necessarily consciously) know what the
difference is, the error. The comparison function actually generates a
physical signal representing the difference or error. A box representing
the comparator is part of the block diagram.
We now have the perceiving and comparing parts of the system. That
leaves only two more major components of the control system to be
explained.
Acting
Steering involves muscles that apply forces to a steering wheel. These
muscles can make the wheel tend to rotate right or left. If a positive
error signal means that the car is too far to the right relative to the
reference condition, then it should be connected to the motor signals
that make the arm muscles twist the wheel to the left. The opposite
should hold for negative error signals. These connections, once made,
will always be correct. You never want to twist the wheel to the left
when the car is already too far left. So if we could wire positive error
signals to one set of muscles and negative error signals to the opposing
set, and if we didn't get the wrong sets hooked up, then the muscles
would always respond in a way that tends to make the error signal
smaller.
Suppose the car is too far to the left, meaning that the perceptual
signal representing it is smaller in magnitude than the reference
signal. This results in a positive error signal, which is wired up to
run the muscles that twist the wheel to the right. If the wheel twists
to the right, the car will move more to the right. The perceptual signal
will get bigger, and the difference between it and the reference signal
will get smaller. The positive error signal will get smaller, and the
steering effort will get smaller. When the car finally reaches just the
right position, the perceptual signal will match the reference signal,
the error signal will become zero, and the steering efforts, in either
direction, will become zero. This system, therefore, will always move
the car from any starting position to whatever position is set by the
reference signal, and then keep it there. To change the position of the
car on the road, all we have to do is change the setting of the
reference signal.
We therefore add another box to the block diagram, called the "output
function." It converts the error signal into a physical effect on the
environment.
There is one more box and one more variable, and then we will be
finished.
The environment function
We can't forget about the car. The car is part of the driver's
environment. When the driver applies a steering effort to the steering
wheel, the car's front wheels are cocked a little, and the car's forward
motion creates a sideward force on the car. This force makes the car
move left or right. That changes the way the car and road look in the
windshield, thus changing the perceptual signal. So the "environment
function" standing for the physical properties of the car is what links
the action of the control system back to its perception, through a
feedback connection. This environment function is the final box in our
block diagram.
Of course there is a lot more to the environment of the driver than just
this environment function (in fact, there's a lot more to the driver
than just this one control system). However, this part of the
environment is the only part of interest when we talk about the control
process, because it completes the closed loop of causation from
perception, to comparison, to action, and back to perception again. This
closed loop is what makes the control system kind of organization
fundamentally different from either of the two conventional sorts of
organization we have discussed.
The last element of this block diagram will complete the model.
The disturbance
Because of the closed loop connection just discussed, the controlled
variable is obviously affected by the actions of the control system. But
in a real environment, the controlled variable is also affected by other
influences, just as the position of the car in its lane is affected by
anything that can apply a sideward force to the car, like a crosswind or
a tilt in the road. We represent the sum of all such independent effects
as a single equivalent disturbance, adding its effects directly to the
controlled variable. No model of a control system is complete without a
representation of the disturbance, because it is the way actions vary in
response to disturbances that provides strong evidence that we are
dealing with a control system.
Here is the completed block diagram:
Fig. 1. The Basic PCT control system
The grey bar across the diagram separates the active control system (above)
from the environment (below). The red lines show the closed causal loop of
control.. Small circles in the environment show where physical variables can
be measured: an output quantity, an input quantity, and a disturbing quantity.
The green lines indicate effects of independent variables: the reference
signal and the disturbing quantity. The Input Function converts a sensed
variable in the environment to a signal representing it inside the system; the
Output Function converts the error signal into a physical effect on the
environment.
The illusion of stimulus and response
Suppose the driver is successfully maintaining his perception of the
car's position in a close match to the reference signal. On a windless
day and on a flat straight road, scarcely any action will be required.
But if a crosswind springs up, it will apply a sideward force to the
car, making it drift to one side. That will cause the perceptual signal
to become different from the reference signal, creating an error signal
that produces an action that tends to correct the error. If the control
system is very sensitive to small errors, it won't take much of an error
to produce an output large enough to prevent any further drift of the
car to one side. In fact, the error caused by the crosswind can be too
small to notice, if the driver is very skillful: the deviation of the
car will be kept very small.
What we see from outside the system is that the crosswind pushes
sideways on the car and the front wheels of the car immediately cock
into the wind, preventing any important change in the car's path. It
looks just as if the car is being stimulated by the wind, and is
responding by turning its front wheels into the wind. Of course we know
that neither the car nor the driver can sense the crosswind; this
appearance of stimulus and response is an illusion. The true explanation
is a little more complicated than the stimulus-response explanation
would be, but not much more complicated.
But we can see now how the impression that stimuli cause responses could
arise, even if the system in question is really a control system that
works as just described.
The illusion of planned action
Suppose we observe that the driver of the car spends some time driving
in a straight line, then turns the car onto another road, then another,
and finally turns it into a driveway in front of a house, where the car
stops. Each time the car turns we can see, as external observers, that
it turns because the front wheels of the car turn for a while and then
straighten out again. And we can see that the front wheels turn because
the driver exerts changing forces on the steering wheel.
When we ask how the driver does this, we may decide that there are
higher levels of organization in the driver's brain which plan out a
series of actions that will bring the car, by a familiar route, to its
home driveway. Since we saw a particular pattern of steering actions, it
is natural to suppose that these higher centers plan and generate this
pattern, via signals relayed to the muscles that actually do the
steering.
This would be an entirely reasonable view if, in fact, the same actions
always occurred when the same path was taken. But this is not really
what happens.
To see what really happens, we have to observe this finding-the-way-home
behavior in much more detail than is usually seen. Instead of seeing the
path as simply a series of left and right turns, we have to look on it
as a continuous dynamic process, with the car always weaving a little
left and right, being influenced by its own momentum and by external
forces that are always acting on it. We have to realize that the tires
are always slipping a little, that the camber of the road tends to make
the car veer downhill, and that the driver's own steering efforts don't
come out exactly right every time. And there's always that pesky
crosswind, pushing this way and that, and then perversely not pushing at
all.
In truth, if we could record the muscle tensions involved in driving the
car home, and then, starting again in the same place and with the same
orientation, play them back with infinite precision, we would, long
before the car got to the driveway, find it in someone's front yard or
mashed into a telephone pole. There can be no plan of _action_ precise
enough to carry out this process that the driver accomplishes every day.
What we really see is not a series of repeated actions that have
repeated consequences, but a series of _variable_ actions that have
repeated consequences. If the actions did not vary exactly as they do,
there is no way that the consequence, ending up in the driveway, could
repeat.
Control theory explains how it is that the driver can, in fact, form a
plan that will result in making all those left and right turns and
ending up in the driveway every time. And at the same time it explains
why it is that the actions are always a little different each time.
The explanation is simply that the planning level of the brain plans not
actions, but perceptions. The driver's brain, at the level at which it
controls the car's motion, receives signals that tell it "Now perceive a
smooth turn to the left with the car remaining in the right lane. Now
perceive continuing in a straight line in your lane. Now perceive a
right turning happening, still properly centered, and a left turn, and
another left turn, and the final turn right into the driveway."
These are requests for perceptions, not commands for actions. They are,
in fact, reference signals. The higher system, once it has specified
what the control system is to perceive, has no more to do with creating
those perceptions. The closed causal loop takes care of operating the
steering wheel so that the actual perceptions continue to match the
reference perceptions, even as the reference perceptions change. At the
same time, it alters the actions as needed to counteract the effects of
any and all disturbances that could make the perception depart from the
reference perception.
So of course we see the front wheels turning left and right in just the
way needed to follow the designated path. But we also see them turning a
little more and a little less than the average amount, and sometimes a
lot more and a lot less, because this is what is required, in the real
world, to keep the perceptions following the changes that are requested
from above.
Conclusion
There is much more to Perceptual Control Theory than given in the brief
sketch above. There are ideas about hierarchies of perception and
control, about learning as a process of reorganization. There are
computer demonstrations and experiments that explore some of the simpler
kinds of control systems, interactively. Most important, there is a
group of people scattered over the world who have taken up this theory
and devote much of their time to it, communicating largely through the
internet. There are even a few places, scattered here and there, where
students are being taught PCT in one or two university courses, even to
the point where a few PhDs have been granted. Every few days another
person is drawn into this discussion, and joins the effort to explore
PCT further, and apply it in new fields.
PCT has not yet become an influential part of the mainstreams of
behavioral science. But it will.
To find out more about this group, and about PCT,
click here
Papers available here:
On Computing Output