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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blaquière, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.
Lewin, J.,Decoy in Pursuit Evasion Games, Stanford University, PhD Dissertation, 1973.
Isaacs, R.,Differential Games: Their Scope, Nature and Future, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.
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.
Wilson, D. J.,On a Nonsingular Surface of a Differential Game, Journal of Optimization Theory and Applications, Vol. 9, No. 5, 1972.
Author information
Authors and Affiliations
Additional information
Communicated by J. V. Breakwell
The author is grateful to Professor J. V. Breakwell for his criticism and valuable remarks.
Rights and permissions
About this article
Cite this article
Lewin, J. The bang-bang-bang problem revisited. J Optim Theory Appl 18, 429–432 (1976). https://doi.org/10.1007/BF00933822
Issue Date:
DOI: https://doi.org/10.1007/BF00933822