Abstract
A differential game in which nonterminating play is assigned a fixed value is examined. The solution exhibits a new kind of singular surface which an optimal path takes an infinite time to cross. By playing nonoptimally in a sufficiently small neighborhood of this surface, the player who prefers the optimal (terminating) value to the value of nonterminating play can force the state across this surface and obtain a value arbitrarily close to the optimal.
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References
Isaacs, R. Differential Games: Their Scope, Nature, and Future, Journal of Optimization Theory and Applications, Vol. 3, No. 5, 1969.
Isaacs, R.,Differential Games, John Wiley and Sons, New York, 1965.
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.
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Communicated by G. Leitmann
This work was carried out with the support of a CSIRO postgraduate studenship.
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Wilson, D.J. On a nonsingular singular surface of a differential game. J Optim Theory Appl 9, 344–358 (1972). https://doi.org/10.1007/BF00932933
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DOI: https://doi.org/10.1007/BF00932933