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A conjugate-point condition for a class of differential games

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Abstract

A conjugate-point necessary condition is derived for a class of differential games. This is done by considering the conjugate-point condition for the minimum problem and maximum problem associated with a differential game. Two definitions of a conjugate point and two conjugate-point necessary conditions result. These two definitions and necessary conditions are shown to be equivalent and are combined into one definition and one necessary condition.

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References

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Authors and Affiliations

  1. Northwestern University, Evanston, Illinois

    W. E. Schmitendorf (Assistant Professor of Mechanical Engineering)

  2. Purdue University, Lafayette, Indiana

    S. J. Citron (Professor of Aeronautics, Astronautics, and Engineering Sciences)

Authors
  1. W. E. Schmitendorf
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  2. S. J. Citron
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Additional information

Communicated by L. D. Berkovitz

This research was primarily supported by the National Science Foundation under Traineeship No. 1721-80-282 and Grant No. GK-3341. Additional support was obtained from NASA Institutional Grant No. NGR-15-005-021.

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Schmitendorf, W.E., Citron, S.J. A conjugate-point condition for a class of differential games. J Optim Theory Appl 4, 109–121 (1969). https://doi.org/10.1007/BF00927416

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  • DOI: https://doi.org/10.1007/BF00927416

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