A MATHEMATICAL FORMULATION OF VARIATIONAL PROCESSES OF ADAPTIVE TYPE
Abstract
The questions discussed belong to two fields which formerly were quite disjoint, the classical theory of probability and the classical calculus of variations. That there is now considerable overlap is due to the rise in scientific interest in the field of control processes. Although it is only within the last few years that the theory of feedback control has penetrated the academic curriculum and become a respectable member of the mathematical community, the conventional formulation is already far outmoded. In order to treat current and future problems of any significance, it is absolutely essential to introduce stochastic elements. These, however, enter in entirely novel ways, not in the fairly well understood fashion of conventional stochastic processes, but in connection with 'learning processes,' or adaptive processes. It is shown that the functional equation technique of dynamic programming can be used to treat adaptive control processes, and that continuous processes can be defined in terms of the discrete versions.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 19, 1960
- Accession Number
- AD0616667
Entities
People
- Richard E. Bellman
Organizations
- RAND Corporation