Adaptation Implies Internal Model

TL;DR

This paper proves that for a system to adapt to a class of signals, it must internally generate those signals, highlighting a fundamental link between adaptation and internal modeling.

Contribution

It establishes a theoretical connection showing that adaptation implies the presence of an internal model within the system, without assuming robustness or specific system partitioning.

Findings

Adaptation requires an internal model capable of generating the signals.

No need for robustness assumptions or explicit plant-controller separation.

The result applies under suitable technical assumptions.

Abstract

This note provides a simple result showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, then S must necessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components.