Search results

Mathematical models (often differential equations) in Modern Control Theory assume “deterministic interaction” between elements of the system. Management systems, in general, do not possess this property. In this paper we employ Beer's ideas to define special quantities and corresponding mathematical methods by which we are able to adapt non‐deterministic interaction for feedback control treatment.

In the construction of Beer's Predictive Model for control of operations in “complex probabilistic systems” a major exercise is the adjustment of resources to meet current productivity values so as to stabilize overall system output. There arise, however, certain theoretical problems in this adjustment exercise and this communication examines some of them.

The Use of Beer's Predictive Model in classifying incoming jobs into achievement groups is basically a pattern recognition problem. Pattern recognition, in modern technology, is a quantitative affair. Following Beer's views on the job‐classification issue, consideration is given to some non‐numerical approaches as well as to the quantitative approach to the problem.

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.