Pursuit-evasion differential games with Gr-constraints on controls

IF 0.3 Q4 MATHEMATICS
B. Samatov, A. Akbarov, B. I. Zhuraev
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引用次数: 2

Abstract

In the paper, a pursuit-evasion differential game is considered when controls of the players are subject to differential constraints in the form of Grönwall's integral inequality. The strategy of parallel pursuit (briefly, $\Pi$-strategy) was introduced and used by L.A. Petrosyan to solve simple pursuit problems under phase constraints on the states of the players in the case when control functions of both players are chosen from the class $L_\infty$. In the present work, the $\Pi$-strategy is constructed for a simple pursuit problem in the cases when control functions of both players are chosen from different classes of the Grönwall type constraints, and sufficient conditions of capture and optimal capture time are found in these cases. To solve the evasion problem, we suggest a control function for the Evader and find sufficient conditions of evasion. In addition, an attainability domain of the players is constructed and its conditions of embedding in respect to time are given. Results of this work continue and extend the works of R. Isaacs, L.A. Petrosyan, B.N. Pshenichnyi, A.A. Chirii, A.A. Azamov and other researchers, including the authors.
控制上有gr约束的追击-逃避微分对策
本文以Grönwall的积分不等式的形式考虑了参与者的控制受到微分约束时的追逃微分对策。平行追击策略(简称$\Pi$ -策略)是由L.A. Petrosyan提出的,用于解决当两个玩家的控制函数都从$L_\infty$类中选择时,玩家状态有相位约束的简单追击问题。本文针对一个简单的追捕问题,在Grönwall类型约束的不同类别中选择双方的控制函数时,构造了$\Pi$ -策略,并找到了捕获的充分条件和最优捕获时间。为了解决规避问题,我们提出了规避器的控制函数,并找到了规避的充分条件。此外,构造了参与者的可达域,并给出了其随时间的嵌入条件。这项工作的结果延续并扩展了R. Isaacs、L.A. Petrosyan、B.N. Pshenichnyi、A.A. Chirii、A.A. Azamov和其他研究人员(包括作者)的工作。
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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