A model for self‐organizing systems

Abstract

Considers a conceptual model that leads to the notions of a “distance function” g(t) and that of a “controlled‐disturbance function” δ(t)=h(g(t)). Using these notions we begin a mathematical theory of a system that is self‐organizing to achieve a given state of affairs in a given environment. Obtains, in terms of the functions δ(t) and g(t), a condition under which the system always progresses towards the goal. We also establish the form of expression for the distance function g(t). This comes as a major tool in the proofs of the so‐called goal‐state‐description theorems. These theorems have results that facilitate the determination of the “working functions” of the self‐organizing system (SOS). When they exist, the “working functions” specify a goal‐path for the SOS to learn to adopt.