On the lower alternating integral of Pontryagin in linear differential games of pursuit

In this article the concept of the lower alternating integral of Pontryagin, which differs from the analogous concept of A. Azamov (Mat. Sb. (N.S.), 1982, v. 118(160), № 3, p. 422–430), is introduced. The properties of this object are studied in comparison with those of the alternating integral of Pontryagin. A procedure is given for application of the lower alternating integral of Pontryagin to linear differential games of pursuit, with special consideration for the question of using the lower alternating integral of Pontryagin when there are countably many measurements of the phase vector. The results are illustrated in two known differential games: “the boy and the crocodile” and the “control example of Pontryagin”.
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