Perceptual control theory

PCT has roots in insights of Claude Bernard and 20th century control systems engineering and cybernetics. Classical negative feedback control was worked out by engineers in the 1930s and 1940s,[3][4] and further developed by Wiener,[5] Ashby,[6] and others in the early development of the field of cybernetics. PCT was originated as a distinct field, and given its present form and experimental methodology, by William T. Powers.[2][7]

Powers recognized that to be purposeful implies control, and that the concepts and methods of engineered control systems could be applied to biological control systems. A key insight is that the variable that is controlled is not the output of the system (the behavioral actions), but its input, that is, a sensed and transformed function of some state of the environment that could be affected by the control system's output. Because some of these sensed and transformed inputs appear as consciously perceived aspects of the environment, Powers labelled the controlled variable "perception". The theory came to be known as "Perceptual Control Theory" or PCT rather than "Control Theory Applied to Psychology" because control theorists often assert or assume that it is the system's output that is controlled.[8] In PCT it is the internal representation of the state of some variable in the environment—a "perception" in everyday language—that is controlled.[9] The basic principles of PCT were first published by Powers, Clark, and MacFarland as a "general feedback theory of behavior" in 1960,[10] with credits to cybernetic authors Wiener and Ashby, and has been systematically developed since then in the research community that has gathered around it.[11] Initially, it was overshadowed by the promises of the 'Cognitive revolution', but is now better known.[12][13][14]

Powers and other researchers in the field point to problems of purpose, causation, and teleology at the foundations of psychology which control theory resolves.[15] From Aristotle through William James and John Dewey it has been recognized that behavior is purposeful and not merely reactive, but how to account for this has been problematic because the only evidence for intentions was subjective. As Powers pointed out, behaviorists following Wundt, Thorndyke, Watson, and others rejected introspective reports as data for an objective science of psychology. Only observable behavior could be admitted as data.[16] There follows from this stance the assumption that environmental events (stimuli) cause behavioral actions (responses). This assumption persists in cognitive psychology, which interposes cognitive maps and other postulated information processing between stimulus and response, but otherwise retains the assumption of linear causation from environment to behavior.[12]

Another, more specific reason that Powers observed for psychologists' rejecting notions of purpose or intention was that they could not see how a goal (a state that did not yet exist) could cause the behavior that led to it. PCT resolves these philosophical arguments about teleology because it provides a model of the functioning of organisms in which purpose has objective status without recourse to introspection, and in which causation is circular around feedback loops.[17]

A simple negative feedback control system is a cruise control system for a car. A cruise control system has a sensor which "perceives" speed as the rate of spin of the drive shaft directly connected to the wheels. It also has a driver-adjustable 'goal' specifying a particular speed. The sensed speed is continuously compared against the specified speed by a device (called a "comparator") which subtracts the currently sensed input value from the stored goal value. The difference (the error signal) determines the throttle setting (the accelerator depression), so that the engine output is continuously varied to prevent the speed of the car from increasing or decreasing from that desired speed as environmental conditions change.

If the speed of the car starts to drop below the goal-speed, for example when climbing a hill, the small increase in the error signal, amplified, causes engine output to increase, which keeps the error very nearly at zero. If the speed begins to exceed the goal, e.g. when going down a hill, the engine is throttled back so as to act as a brake, so again the speed is kept from departing more than a barely detectable amount from the goal speed (brakes being needed only if the hill is too steep). The result is that the cruise control system maintains a speed close to the goal as the car goes up and down hills, and as other disturbances such as wind affect the car's speed. This is all done without any planning of specific actions, and without any blind reactions to stimuli. Indeed, the cruise control system does not sense disturbances such as wind pressure at all, it only senses the controlled variable, speed. Nor does it control the power generated by the engine, it uses the 'behavior' of engine power as its means to control the sensed speed.

The same principles of negative feedback control (including the ability to nullify effects of unpredictable external or internal disturbances) apply to living control systems.[5] The thesis of PCT is that animals and people do not control their behavior; rather, they vary their behavior as their means for controlling their perceptions, with or without external disturbances. This directly contradicts the historical and still widespread assumption that behavior is the final result of stimulus inputs and cognitive plans.[12][18]

The principal datum in PCT methodology is the controlled variable. The fundamental step of PCT research, the test for controlled variables, begins with the slow and gentle application of disturbing influences to the state of a variable in the environment which the researcher surmises is already under control by the observed organism. It is essential not to overwhelm the organism's ability to control, since that is what is being investigated. If the organism changes its actions just so as to prevent the disturbing influence from having the expected effect on that variable, that is strong evidence that the experimental action disturbed a controlled variable. It is crucially important to distinguish the perceptions and point of view of the observer from those of the observed organism. It may take a number of variations of the test to isolate just which aspect of the environmental situation is under control, as perceived by the observed organism.[19][20]

PCT employs a black box methodology. The controlled variable as measured by the observer corresponds quantitatively to a reference value for a perception that the organism is controlling. The controlled variable is thus an objective index of the purpose or intention of those particular behavioral actions by the organism—the goal which those actions consistently work to attain despite disturbances. With few exceptions, in the current state of neuroscience this internally maintained reference value is seldom directly observed as such (e.g. as a rate of firing in a neuron), since few researchers trace the relevant electrical and chemical variables by their specific pathways while a living organism is engaging in what we externally observe as behavior.[21] However, when a working negative feedback system simulated on a digital computer performs essentially identically to observed organisms, then the well understood negative feedback structure of the simulation or model (the white box) is understood to demonstrate the unseen negative feedback structure within the organism (the black box).[2]

Data for individuals are not aggregated for statistical analysis;[22] instead, a generative model is built which replicates the data observed for individuals with very high fidelity (0.95 or better). To build such a model of a given behavioral situation requires careful measurements of three observed variables:

A fourth value, the internally maintained reference r (a variable ′setpoint′), is deduced from the value at which the organism is observed to maintain q_i, as determined by the test for controlled variables (described at the beginning of this section).

With two variables specified, the controlled input q_i and the reference r, a properly designed control system, simulated on a digital computer, produces outputs q_o that almost precisely oppose unpredictable disturbances d to the controlled input. Further, the variance from perfect control accords well with that observed for living organisms.[23] Perfect control would result in zero effect of the disturbance, but living organisms are not perfect controllers, and the aim of PCT is to model living organisms. When a computer simulation performs with >95% conformity to experimentally measured values, opposing the effect of unpredictable changes in d by generating (nearly) equal and opposite values of q_o, it is understood to model the behavior and the internal control-loop structure of the organism.[17][10][24]

By extension, the elaboration of the theory constitutes a general model of cognitive process and behavior. With every specific model or simulation of behavior that is constructed and tested against observed data, the general model that is presented in the theory is exposed to potential challenge that could call for revision or could lead to refutation.

To illustrate the mathematical calculations employed in a PCT simulation, consider a pursuit tracking task in which the participant keeps a mouse cursor aligned with a moving target on a computer monitor.

The model assumes that a perceptual signal within the participant represents the magnitude of the input quantity q_i. (This has been demonstrated to be a rate of firing in a neuron, at least at the lowest levels.)[24][25] In the tracking task, the input quantity is the vertical distance between the target position T and the cursor position C, and the random variation of the target position acts as the disturbance d of that input quantity. This suggests that the perceptual signal p quantitatively represents the cursor position C minus the target position T, as expressed in the equation p=C–T.

Between the perception of target and cursor and the construction of the signal representing the distance between them there is a delay of Τ milliseconds, so that the working perceptual signal at time t represents the target-to-cursor distance at a prior time, t – Τ. Consequently, the equation used in the model is

1. p(t) = C(t–Τ) – T(t–Τ)

The negative feedback control system receives a reference signal r which specifies the magnitude of the given perceptual signal which is currently intended or desired. (For the origin of r within the organism, see under "A hierarchy of control", below.) Both r and p are input to a simple neural structure with r excitatory and p inhibitory. This structure is called a "comparator".[24] The effect is to subtract p from r, yielding an error signal e that indicates the magnitude and sign of the difference between the desired magnitude r and the currently input magnitude p of the given perception. The equation representing this in the model is:

2. e = r–p

The error signal e must be transformed to the output quantity q_o (representing the participant's muscular efforts affecting the mouse position). Experiments have shown that in the best model for the output function, the mouse velocity V_cursor is proportional to the error signal e by a gain factor G (that is, V_cursor = G*e). Thus, when the perceptual signal p is smaller than the reference signal r, the error signal e has a positive sign, and from it the model computes an upward velocity of the cursor that is proportional to the error.

The next position of the cursor C_new is the current position C_old plus the velocity V_cursor times the duration dt of one iteration of the program. By simple algebra, we substitute G*e (as given above) for V_cursor, yielding a third equation:

3. C_new = C_old + G*e*dt

These three simple equations or program steps constitute the simplest form of the model for the tracking task. When these three simultaneous equations are evaluated over and over with the same random disturbances d of the target position that the human participant experienced, the output positions and velocities of the cursor duplicate the participant's actions in the tracking task above within 4.0% of their peak-to-peak range, in great detail.

This simple model can be refined with a damping factor d which reduces the discrepancy between the model and the human participant to 3.6% when the disturbance d is set to maximum difficulty.

3'. C_new = C_old + [(G*e)–(d*C_old)]*dt

Detailed discussion of this model in (Powers 2008)[23] includes both source and executable code, with which the reader can verify how well this simple program simulates real behavior. No consideration is needed of possible nonlinearities such as the Weber-Fechner law, potential noise in the system, continuously varying angles at the joints, and many other factors that could afflict performance if this were a simple linear model. No inverse kinematics or predictive calculations are required. The model simply reduces the discrepancy between input p and reference r continuously as it arises in real time, and that is all that is required—as predicted by the theory.[17][24]

In the artificial systems that are specified by engineering control theory, the reference signal is considered to be an external input to the 'plant'.[8] In engineering control theory, the reference signal or set point is public; in PCT, it is not, but rather must be deduced from the results of the test for controlled variables, as described above in the methodology section. This is because in living systems a reference signal is not an externally accessible input, but instead originates within the system. In the hierarchical model, error output of higher-level control loops, as described in the next section below, evokes the reference signal r from synapse-local memory, and the strength of r is proportional to the (weighted) strength of the error signal or signals from one or more higher-level systems.[26]

In engineering control systems, in the case where there are several such reference inputs, a 'Controller' is designed to manipulate those inputs so as to obtain the effect on the output of the system that is desired by the system's designer, and the task of a control theory (so conceived) is to calculate those manipulations so as to avoid instability and oscillation. The designer of a PCT model or simulation specifies no particular desired effect on the output of the system, except that it must be whatever is required to bring the input from the environment (the perceptual signal) into conformity with the reference. In Perceptual Control Theory, the input function for the reference signal is a weighted sum of internally generated signals (in the canonical case, higher-level error signals), and loop stability is determined locally for each loop in the manner sketched in the preceding section on the mathematics of PCT (and elaborated more fully in the referenced literature). The weighted sum is understood to result from reorganization.

Engineering control theory is computationally demanding, but as the preceding section shows, PCT is not. For example, contrast the implementation of a model of an inverted pendulum in engineering control theory[27] with the PCT implementation as a hierarchy of five simple control systems.[28]

Perceptions, in PCT, are constructed and controlled in a hierarchy of levels. For example, visual perception of an object is constructed from differences in light intensity or differences in sensations such as color at its edges. Controlling the shape or location of the object requires altering the perceptions of sensations or intensities (which are controlled by lower-level systems). This organizing principle is applied at all levels, up to the most abstract philosophical and theoretical constructs.

The Russian physiologist Nicolas Bernstein[29] independently came to the same conclusion that behavior has to be multiordinal—organized hierarchically, in layers. A simple problem led to this conclusion at about the same time both in PCT and in Bernstein's work. The spinal reflexes act to stabilize limbs against disturbances. Why do they not prevent centers higher in the brain from using those limbs to carry out behavior? Since the brain obviously does use the spinal systems in producing behavior, there must be a principle that allows the higher systems to operate by incorporating the reflexes, not just by overcoming them or turning them off. The answer is that the reference value (setpoint) for a spinal reflex is not static; rather, it is varied by higher-level systems as their means of moving the limbs. This principle applies to higher feedback loops, as each loop presents the same problem to subsystems above it.

Whereas an engineered control system has a reference value or setpoint adjusted by some external agency, the reference value for a biological control system cannot be set in this way. The setpoint must come from some internal process. If there is a way for behavior to affect it, any perception may be brought to the state momentarily specified by higher levels and then be maintained in that state against unpredictable disturbances. In a hierarchy of control systems, higher levels adjust the goals of lower levels as their means of approaching their own goals set by still-higher systems. This has important consequences for any proposed external control of an autonomous living control system (organism). At the highest level, reference values (goals) are set by heredity or adaptive processes.

If an organism controls inappropriate perceptions, or if it controls some perceptions to inappropriate values, then it is less likely to bring progeny to maturity, and may die. Consequently, by natural selection successive generations of organisms evolve so that they control those perceptions that, when controlled with appropriate setpoints, tend to maintain critical internal variables at optimal levels, or at least within non-lethal limits. Powers called these critical internal variables "intrinsic variables" (Ashby's "essential variables").

The mechanism that influences the development of structures of perceptions to be controlled is termed "reorganization", a process within the individual organism that is subject to natural selection just as is the evolved structure of individuals within a species.[30]

This "reorganization system" is proposed to be part of the inherited structure of the organism. It changes the underlying parameters and connectivity of the control hierarchy in a random-walk manner. There is a basic continuous rate of change in intrinsic variables which proceeds at a speed set by the total error (and stops at zero error), punctuated by random changes in direction in a hyperspace with as many dimensions as there are critical variables. This is a more or less direct adaptation of Ashby's "homeostat", first adopted into PCT in the 1960 paper[10] and then changed to use E. coli's method of navigating up gradients of nutrients, as described by Koshland (1980).[31]

Reorganization may occur at any level when loss of control at that level causes intrinsic (essential) variables to deviate from genetically determined set points. This is the basic mechanism that is involved in trial-and-error learning, which leads to the acquisition of more systematic kinds of learning processes.[32]

The reorganization concept has led to a method of psychotherapy called the method of levels (MOL). Using MOL, the therapist aims to help the patient shift his or her awareness to higher levels of perception in order to resolve conflicts and allow reorganization to take place.[33]

The preceding explanation of PCT principles provides justification of how this theory can provide a valid explanation of neural organisation and how it can explain some of the current issues of conceptual models.

Perceptual control theory currently proposes a hierarchy of 11 levels of perceptions controlled by systems in the human mind and neural architecture. These are: intensity, sensation, configuration, transition, event, relationship, category, sequence, program, principle, and system concept. Diverse perceptual signals at a lower level (e.g. visual perceptions of intensities) are combined in an input function to construct a single perception at the higher level (e.g. visual perception of a color sensation). The perceptions that are constructed and controlled at the lower levels are passed along as the perceptual inputs at the higher levels. The higher levels in turn control by adjusting the reference levels (goals) of the lower levels, in effect telling the lower levels what to perceive.[24][32]

While many computer demonstrations of principles have been developed, the proposed higher levels are difficult to model because too little is known about how the brain works at these levels. Isolated higher-level control processes can be investigated, but models of an extensive hierarchy of control are still only conceptual, or at best rudimentary.

Perceptual control theory has not been widely accepted in mainstream psychology, but has been effectively used in a considerable range of domains[41][42] in human factors,[43] clinical psychology, and psychotherapy (the "Method of Levels"), it is the basis for a considerable body of research in sociology,[44] and it has formed the conceptual foundation for the reference model used by a succession of NATO research study groups.[45] It is being taught in several universities worldwide and is the subject of a number of PhD dissertations.[46]

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• Powers, William T. (2008). Living Control Systems III: The fact of control. [Mathematical appendix by Dr. Richard Kennaway. Includes computer programs for the reader to demonstrate and experimentally test the theory.] New Canaan, CT: Benchmark Publications. ISBN 978-0-9647121-8-8.
• Powers, William. T., Clark, R. K., and McFarland, R. L. (1960). "A general feedback theory of human behavior [Part 1; Part 2]. Perceptual and Motor Skills 11, 71–88; 309–323.
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