Differential Games with the Langenhop Type Constrains on Controls

In this article, the concept of a Langenhop type constraint on the controls of players is introduced. The relationship between geometric, Langenhop and integral constraints is investigated. For these three classes, the attainability domains of the players are found by admissible controls. The parallel pursuit strategy ( $$\Pi$$ -strategy) is constructed for differential game of pursuit with Langenhop type constraints and the sufficient solvability conditions of the problem are obtained. To solve the evasion problem, the lower bounds of the convergence, depending on the given parameters, is found. This work develops the works of Isaacs, Petrosjan, Pshenichnyi, Azamov and other researchers, including the authors.

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