That shows its behaviour by a trajectory, with the outcome E
Depending on the properties of T’s trajectory. The outcomes will
Then usually be affected by which of T’s states is the initial one.
How does T’s initial state come into the basic formulation of S.11/4?
If the initial state can be controlled, so that the trajectory can be
Started always from some standardised state, then no difficulty
Arises. (In this connexion the method of S.7/25 may be useful.) It
May however happen, especially if the system is very large, that
T’s initial state cannot be standardised. Does the basic formula-
Tion include this case?
It does; for D, as a vector, can be re-defined to include T’s initial
State. Then the variety brought to E by the variety in T’s initial
State is allotted its proper place in the formulation.
Compound target. It may happen that the acceptable states
η at E may have more than one condition. Thus of a thermostat it
Might be demanded that
(i) it shall usually stay between 36 ° and 37 °C;
(ii) if displaced by + 10 ° it shall return to the allowed range
Within one minute.
This difficulty can be dealt with by the same method as in S.11/
By recognising that E may be a vector, with more than one
component, and that what is acceptable ( η) may be given in the
Form of separate specifications for each component.
Thus, by allowing E to become a vector, the basic formulation
Of S. 11/4 can be made to include all cases in which the target is
Complex, or conditional, or qualified.
Internal complexities. As a last example, showing how
Comprehensive the basic formulation really is, consider the case
In which the major problem seems to be not so much a regulation
217
A N I N T R O D UC T I O N T O C Y B E R NE T I C S
As an interaction between several regulations. Thus a signalman
May have to handle several trains coming to his section simulta-
Neously. To handle any one by itself would be straightforward,
But here the problem is the control of them as a complex whole
Pattern.
This case is in fact still covered by the basic formulation. For
Nothing in that formulation prevents the quantities or states or ele-
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Ments in D, R, T, or E from being made of parts, and the parts
Interrelated. The fact that “D” is a single letter in no way implies
That what it represents must be internally simple or unitary.
The signalman’s “disturbance” D is the particular set of trains
Arriving in some particular pattern over space and time. Other
Arrangements would provide other values for D, which must, of
Course, be a vector. The outcomes E will be various complex pat-
Terns of trains moving in relation to one another and moving away
from his section. The acceptable set η will certainly include a com-
Ponent “no collision” and will probably include others as well. His
Responses R will include a variety of patterns of movements of sig-
Nals and points. T is what is given— the basic matters of geography,
Mechanics, signalling techniques, etc., that lead determinately from
The situation that has arisen and his reaction pattern to outcome.
It will be seen therefore that the basic formulation is capable, in
Principle, of including cases of any degree of internal complexity.
218
Chapter
12
TH E E R ROR -C ONT ROL L E D
R E GULAT OR
In the previous chapter we studied the nature of regulation,
And showed that certain relations and laws must hold if regulation
Is to be achieved. There we assumed that regulation was achieved,
And then studied what was necessary. This point of view, however,
Though useful, hardly corresponds with that commonly used in
Practice. Let us change to a new point of view.
In practice, the question of regulation usually arises in this way:
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