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Differential games of fixed duration with state constraints

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Abstract

We consider differential games of fixed duration with phase coordinate restrictions on the players. Results of Ref. 1 on games with phase restrictions on only one of the players are extended. Using Berkovitz's definition of a game (Ref. 2), we prove the existence and continuity (or Lipschitz continuity) of the value under appropriate assumptions. We also note that the value can be characterized as the viscosity solution of the associated Hamilton-Jacobi-Isaacs equation.

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References

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Authors and Affiliations

  1. Rockwell International Space Systems Division, Downey, California

    K. H. Ghassemi (Staff member)

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  1. K. H. Ghassemi
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Communicated by L. D. Berkovitz

This work comprises a part of the author's PhD Thesis completed at Purdue University under the direction of Professor L. D. Berkovitz. The author wishes to thank Professor Berkovitz for suggesting the problem and many valuable discussions. During the research for this work, the author was supported by a David Ross Grant from Purdue University as well as by NSF Grant No. DMS-87-00813.

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Ghassemi, K.H. Differential games of fixed duration with state constraints. J Optim Theory Appl 68, 513–537 (1991). https://doi.org/10.1007/BF00940068

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