无穷二元微分方程系统的最优追求微分博弈问题

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600821

G. I. Ibragimov, X. Sh. Qo’shaqov, A. A. Muxammadjonov

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引用次数: 0

摘要

摘要我们研究了一个无穷二元微分方程系统的微分博弈问题。追逐者和逃避者的控制函数都受到积分约束。追逐者试图使系统的状态到达希尔伯特空间 \(l_{2}\)的原点，而逃避者的目标则相反。我们得到了最优追逐时间方程，并构建了追逐者的最优控制。此外，还求解了一个辅助最优控制问题，以证明本文的主要结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Optimal Pursuit Differential Game Problem for an Infinite System of Binary Differential Equations

Abstract

We study a differential game problem for an infinite system of binary differential equations. The control functions of pursuer and evader are subjected to integral constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space \(l_{2}\) and the aim of the evader is opposite. An equation for the optimal pursuit time is obtained and optimal controls of players are constructed. Also, an auxiliary optimal control problem is solved to prove the main result of the paper.

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.