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On the contradiction of bang-bang-bang surfaces in differential games

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Abstract

The recently reported phenomenon ofbang-bang-bang surfaces (BBBS) appears to contradict the known theory of differential games. This paper indicates what seems to be the mathematical basis for removing this contradiction, as it applies to the example used by Isaacs to introduce the notion of BBBS. Also, a novel example of multiple candidates for solutions to a differential game is presented.

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References

  1. Isaacs, R.,Differential Games: Their Scope, Nature, and Future, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.

  2. Ciletti, M. D.,Norm-Invariant Systems—Differential Games, IEEE Transactions on Automatic Control, Vol. AC-13, No. 6, 1968.

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Authors and Affiliations

  1. Frank J. Seiler Research Laboratory (OAR), USAF Academy, Colorado

    Michael D. Ciletti (Research Associate and Assistant Professor of Electrical Engineering)

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  1. Michael D. Ciletti
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Communicated by J. V. Breakwell

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Ciletti, M.D. On the contradiction of bang-bang-bang surfaces in differential games. J Optim Theory Appl 5, 163–169 (1970). https://doi.org/10.1007/BF00927713

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  • DOI: https://doi.org/10.1007/BF00927713

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