Differential Games with the Langenhop Type Constrains on Controls
Bahrom SamatovV.I. Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences and Namangan State University, Namangan, UzbekistanNargiza UmaraliyevaNamangan State University, Namangan, UzbekistanS. I. UralovaNamangan State University, Namangan, Uzbekistan
ABI
Abstract
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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