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The bang-bang-bang problem revisited

  • J. Lewin
Technical Note

Abstract

The solution given by Isaacs to the bang-bang-bang problem is shown to be a solution in aweak sense only. A solution in a stronger sense is demonstrated involving the notions of extended closed-loop strategies and of extended value-function. The bang-bang-bang singular surface is interpreted in a new way.

Key Words

Game theory differential games optimal strategies closed-loop controls bang-bang-bang problem 

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References

  1. 1.
    Blaquière, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.Google Scholar
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    Lewin, J.,Decoy in Pursuit Evasion Games, Stanford University, PhD Dissertation, 1973.Google Scholar
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    Isaacs, R.,Differential Games: Their Scope, Nature and Future, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.Google Scholar
  4. 4.
    Ciletti, M. D.,On the Contradiction of Bang-Bang-Bang Surface in Differential Games, Journal of Optimization Theory and Applications, Vol. 5, No. 3, 1970.Google Scholar
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    Wilson, D. J.,On a Nonsingular Surface of a Differential Game, Journal of Optimization Theory and Applications, Vol. 9, No. 5, 1972.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • J. Lewin
    • 1
  1. 1.Armament Development AuthorityMinistry of DefenseHaifaIsrael

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