Adaptation and regulation with signal detection implies internal model

Details Adaptation and regulation with signal detection implies internal model Adaptation and regulation with signal detection implies internal model

2003-09-16

arxiv.org/abs/q-bio/0309003v1

Biology

Quantitative Biology

Quantitative Methods

See http://www.math.rutgers.edu/~sontag for related work; to appear in Systems and Control Letters

Scientific paper

This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily 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. Instead, one assumes that a ``signal detection'' property holds. The result was motivated by questions of adaptation in bacterial chemotaxis, but the general mathematical principle is of wide applicability.

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