Cover: Reduction of dimensionality, dynamic programming, and control processes.

Reduction of dimensionality, dynamic programming, and control processes.

Published 1960

by Richard Ernest Bellman, Robert E. Kalaba

Purchase Print Copy

 Format Price
Add to Cart Paperback12 pages $15.00

A discussion of the occurrence of processes having state vectors of high dimension, a major difficulty in achieving a successful systematic approach to the study of control processes by means of dynamic-programming theory. However difficult the problem is for systems ruled by a finite set of differential equations, it is several orders of magnitude more complex for systems of infinite dimensionality and for systems with time lags. By combining a technique for dealing with finite- dimensional systems and various methods of successive approximations and quasilinearization, certain classes of control processes associated with infinite dimensional systems can be treated. The ideas are illustrated by examining not only the control of a system involving a time lag, but also the control of a thermal system. 12 pp.

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.