Abstract
On a fixed time interval we consider zero-sum nonlinear differential games for which the integrand in the criterion functional is a sufficiently strongly convex-concave function of chosen controls. It is shown that in our setting there exists a saddle point in the class of programmed strategies, and a minimax principle similar to Pontryagin's maximum principle is a necessary and sufficient condition for optimality. An example in which the class of games under study is compared with two known classes of differential games is given.
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Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 725–743, November, 1997.
Translated by N. K. Kulman
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Ivanov, G.E. Saddle point for differential games with strongly convex-concave integrand. Math Notes 62, 607–622 (1997). https://doi.org/10.1007/BF02361299
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DOI: https://doi.org/10.1007/BF02361299