A model for self-organizing systems
Considers a conceptual model that leads to the notions of a "distance function" g(t) and that of a "controlled-disturbance function" delta(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 5(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.
modelling cybernetics systems analysis