On linear differential games with integral constraints

Pursuit game problems for linear systems with integral constraints for controls are studied. The proposed scheme uses the ideas of the method of resolving functions. An analog of the Pontryagin condition is formulated, which makes it possible to establish sufficient conditions for the termination of the differential game in some guaranteed time by using the measurable choice theorem for constructing the pursuer’s control. The obtained results are illustrated by typical examples of game situations: simple motion and Pontryagin’s test case.

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