Optimal Trajectories for Quadratic Variational Processes Via Invariant Imbedding.

Harriett H. Natsuyama, Robert E. Kalaba

ResearchPublished 1969

An improved derivation of the initial-value problem of invariant imbedding for a quadratic variational problem is provided. Although typical approaches lead to characterizing the optimizers as solutions of Euler differential equations subject to certain boundary conditions, numerical solution of such problems is far from routine. When optimizers are described as solutions of initial-value problems, however, there are inherent computational advantages. The transformation does not require the use of Euler equations, dynamic programming, or the Pontryagin principle; only ordinary differential equations are employed. The Cauchy problem provides a one-sweep integration procedure. Various extensions are indicated. 21 pp. Refs. (KB)

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1969
  • Document Number: RM-5929-PR

Citation

Chicago Manual of Style

Natsuyama, Harriett H. and Robert E. Kalaba, Optimal Trajectories for Quadratic Variational Processes Via Invariant Imbedding. Santa Monica, CA: RAND Corporation, 1969. https://www.rand.org/pubs/research_memoranda/RM5929.html.
BibTeX RIS

This publication is part of the RAND research memorandum series. The research memorandum series, a product of RAND from 1948 to 1973, included working papers meant to report current results of RAND research to appropriate audiences.

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 www.rand.org/pubs/permissions.

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.