Training, stability and control

This paper presents a system-theoretic approach to the analysis of the problem of training formally relating it to the control of an abstract dynamic system, the “adaption automaton” of the trainee. The utility of this formulation and the possibility of basing real training strategies upon it are discussed, and it is argued that further constraints upon the automaton are both necessary, and available, in so far as the theory corresponds to practical reality. The minimal constraints generate an extended theory in which training is related to the stability of the adaption automaton. More practical constraints lead to theoretical foundations for strategies of “feedback” or “adaptive” training. Corresponding to each set of constraints a “training theorem” is proved which demonstrates that the constraint is adequate to lead to a simple universal training strategy.Although this paper is highly theoretical it is argued that the formal concepts introduced correspond to intuitive models of the phenomena of learning and training which are implicit in the design of many training systems. It is hoped that the formal analysis will throw new light on these implicit assumptions and help to clarify discussion of practical approaches to training, including the possibility of “computer-aided instruction” given on our present level of knowledge of human cognitive skills or individual students.