Abstract
Abstract A positional differential game for a linear system is considered. This game differs from games previously studied in the literature in that it does not assume geometrical constraints on the controls and the disturbances, but instead imposes integral constraints on the samples of the disturbance. The existence of an optimal strategy is established and a method of construction is suggested. Counterstrategies are constructed that generate the worst-case realizations of the disturbance. It is established that this differential game has a value and a saddle point.
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