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An extension of the Caratheodory—Kalman variational method

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Abstract

We apply the Caratheodory method to variational problems posed in a Banach space. A treatment of the problem of Lagrange leads to the necessary conditions for constrained optimal control problems. Specialization of the space leads to recovery of the usual necessary conditions and extension of the necessary conditions to a class of problems for systems with distributed parameters. The spaces are not restricted to be reflexive, thus permitting consideration of control problems in queuing theory and transport theory. An application to certain queuing processes completes the paper.

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Authors and Affiliations

  1. Northwestern University, Evanston, Illinois

    Arthur Wouk (Associate Professor of Applied Mathematics and Engineering Sciences)

  2. Argonne National Laboratory, Lemont, Illinois

    Arthur Wouk (Associate Professor of Applied Mathematics and Engineering Sciences)

Authors
  1. Arthur Wouk
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Additional information

Communicated by M. R. Hestenes

This work was performed partly under the auspices of the US Atomic Energy Commission and partly under National Science Foundation Grant No. GP-3900.

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Wouk, A. An extension of the Caratheodory—Kalman variational method. J Optim Theory Appl 3, 2–33 (1969). https://doi.org/10.1007/BF00929539

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  • DOI: https://doi.org/10.1007/BF00929539

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