Part 2. Feedback and Control

Form of a Control System

A control system, in the sense used in Perceptual Control Theory, consists of a feedback loop in which a scalar-valued signal called the "perceptual signal" is generated from a complex of values of properties in the world outside the control unit. The perceptual signal is compared with a reference value that also comes from outside the control unit. The difference between the perceptual signal and the reference signal is the "error" in the control unit, and it provided the input to an "output function" that affects the entities in the outer world that contribute to the perceptual signal. These entities are also affected by external influences called "disturbances," the impact of which on the value of the perceptual signal is countered by the effect of the output signal of the control unit. The perceptual signal itself can serve as one of the complex of values that contribute to the perceptual signal of another control unit.

Vector Representation

The perceptual function p=p(s1,...,sk) defines the relationship between the value of the perceptual signal and the values of the sensory input values. It therefore defines the Controlled Environmental Variable.

In simple simulations, a useful form for the perceptual function is one often used in neural network simulations: p=f(c1*s1+c2*s2+...+ck*sk), where f is a saturating non-linear function (e.g. logistic). The set of weights{c1,...ck} defines a vector in the "Outer World" space. This vector is the Controlled Environmental Variable. It can be seen as a projector of the perceptual signal into the "Outer World" space. This vector representation will be important in what follows.