# Good regulator

The **good regulator** is a theorem conceived by Roger C. Conant and W. Ross Ashby that is central to cybernetics. It is stated that "every good regulator of a system must be a model of that system".^{[1]} That is, any regulator that is maximally successful and simple must be isomorphic with the system being regulated. This result 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 mapping from the states of the system to the states of the regulator. The minimum is obtained when the map is an isomorphism, that is, when the regulator models 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 systems.

The theorem does not explain what it takes for the system to become a good regulator. The problem of creation of good regulators is addressed by practopoietic theory.

When restricted to the ODE (Ordinary Differential Equations) subset of control theory, it is referred to as the internal model principle, which was first articulated in 1976 by B. A. Francis and W. M. Wonham.^{[2]} 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).^{[3]}

## See also

- Analogy#Mathematics
- Variety (cybernetics)
- Practopoiesis
- Internal model (motor control)
- W. Ross Ashby

## References

- ↑ Conant and Ashby, "Every good regulator of a system must be a model of that system",
*Int. J. Systems Sci.*, 1970, vol**1**, No 2, pp. 89–97 - ↑ B. A. Francis and W. M. Wonham, "The internal model principle of control theory",
*Automatica***12**(1976) 457–465. - ↑ Jan Swevers, "Internal model control (IMC)", 2006

## External links

- Daniel L. Scholten discusses in his "Every Good Key Must Be A Model Of The Lock It Opens"
- The Good-Regulator Project by Daniel L. Scholten