| 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. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 725–743, November, 1997. Translated by N. K. Kulman |
