The good regulator is a
theorem conceived by Roger C. Conant and
W. Ross Ashby
W. Ross Ashby (6 September 1903 – 15 November 1972) was an English psychiatrist and a pioneer in cybernetics, the study of the science of communications and automatic control systems in both machines and living things. His first name was not ...
that is central to
cybernetics. Originally stated that "every good regulator of a system must be a model of that system", but more accurately, every good regulator must contain a model of the system. That is, any
regulator that is maximally simple among optimal regulators must behave as an image of that system under a
homomorphism; while the authors sometimes say 'isomorphism', the mapping they construct is only a homomorphism.
Theorem
This theorem is obtained by considering the
entropy of the variation of the output of the controlled system, and shows that, under very general conditions, that the entropy is minimized when there is a (deterministic)
mapping from the
states of the
system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expresse ...
to the states of the regulator. The authors view this map
as making the regulator a 'model' of the system.
With regard to the brain, insofar as it is successful and efficient as a regulator for survival, it must proceed, in learning, by the formation of a model (or models) of its environment.
The theorem is general enough to apply to all regulating and self-regulating or
homeostatic system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expresse ...
s.
The theorem does not explain what it takes for the system to become a good regulator. In cybernetics, the problem of creating good regulators is addressed by the
ethical regulator theorem, and by the theory of
practopoiesis. The construction of good regulators is a general problem for any system (e.g., an automated information system) that regulates some domain of application.
When restricted to the
ordinary differential equation (ODE) subset of
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
, it is referred to as the
internal model principle, which was first articulated in 1976 by B. A. Francis and W. M. Wonham. In this form, it stands in contrast to classical control, in that the classical
feedback loop fails to explicitly model the controlled system (although the classical controller may contain an implicit model).
[Jan Swevers,]
Internal model control (IMC)
{{Webarchive, url=https://web.archive.org/web/20170830033243/https://people.mech.kuleuven.be/~jswevers/h04x3a/lecture_c9_c10.pdf , date=2017-08-30 ", 2006
See also
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Analogy#Mathematics
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Map–territory relation
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Variety (cybernetics)
In cybernetics, the term variety denotes the total number of distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity. Varie ...
*
Internal model (motor control)
*
Ethical regulator
*
W. Ross Ashby
W. Ross Ashby (6 September 1903 – 15 November 1972) was an English psychiatrist and a pioneer in cybernetics, the study of the science of communications and automatic control systems in both machines and living things. His first name was not ...
References
Cybernetics