Back to Reading RoomA 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 discriminative stimulus appeared -- the next time the driver saw the street sign saying "Lincoln Street." Maybe the driver's girlfriend 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 accommodate 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.

Copyright 2003 William T. Powers