Good regulator theorem

And while the authors sometimes say the regulator and regulated are 'isomorphic', the mapping they construct is only a homomorphism, meaning the model can lose information about the entity that is modeled.

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

The theorem is general enough to apply to all regulating and self-regulating or homeostatic systems.

Five variables are defined by the authors as involved in the process of system regulation.

of events concerning the system to be regulated in order to render in satisfactory outcomes

of events concerning the system that exist outside of the regulator, then the set

of events in the regulator may fail to account for the total variable disturbances

which in turn may cause errors that lead to outcomes that are not satisfactory to the system (as illustrated by the events in the set

The theorem does not explain what it takes for the system to become a good regulator.

Moreover, although highly cited, some concerns have been raised that the formal proof does not actually fully support the statement in the paper title.

When restricted to the ordinary differential equation (ODE) subset of control theory, it is referred to as the internal model principle, which was first articulated in 1976 by B.