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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On the Pursuit Problem for a Quasilinear Differential Game of Neutral Type

Author(s):

Edgor Mirzoevich Mukhsinov

Tajikistan State University of Law, Business, and Politics (TSULPB, Tajikistan)
associate professor of the department of mathematical disciplines and modern natural science
735700, Tajikistan, Hudjand, 17 distr., 2.

yodgor.mukhsinov@gmail.com

Abstract:

In the field of the theory of differential games, when the game takes place in a finite-dimensional space, the fundamental work was carried out by academicians L. S. Pontryagin and N. N. Krasovskiy. In the works of N. N. Krasovskiy and his co-workers, positional differential games are investigated. In the approach of L. S. Pontryagin and his co-workers, the differential game is considered separately from the point of view of the pursuer and from the point of view of the evader, which inevitably links the differential game with two different problems. In this paper, we consider the pursuit problem in the sense of L. S. Pontryagin for a quasilinear differential game of neutral type in a Banach space. Two theorems on sufficient conditions for the solvability of the pursuit problem are proved. For one example, a linear differential game described by a differential equation of neutral type is investigated. Sufficient conditions that ensure the solvability of the pursuit problem are found.

Keywords

References:

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