Convergence properties of associative memory storage for learning control systems

The associative memory system for learning control systems developed by J. S. Albus is described, and the underlying mathematical algorithm is interpreted as a process of dropping perpendiculars to a series of hyperplanes. The convergence of this process is investigated for what is called «cyclic training» in some detail. Here the algorithm either converges to a fixed point or tends to a «limit cycle». «Random training» is also possible in practice, and, in certain circumstances, the algorithm will also converge to a fixed point. In general, however, it is possible at the present time only to make certain conjectures about the convergence of the random training process to so-called «capture zones». Illustrations of the various concepts developed in the paper are given in Appendices.