{"title":"关于两个刚性协调逃避者的简单追逐问题","authors":"N. Petrov","doi":"10.35634/2226-3594-2022-59-05","DOIUrl":null,"url":null,"abstract":"In a finite-dimensional Euclidean space, the problem of pursuit by a group of pursuers of two evaders described by a system of the form $$\\dot z_{ij} = u_i - v,\\quad u_i, v \\in V $$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is unit ball centered at zero, target sets are the origin. The goal of the pursuers' group is to capture at least one evader by two pursuers or to capture two evaders. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On one simple pursuit problem of two rigidly coordinated evaders\",\"authors\":\"N. Petrov\",\"doi\":\"10.35634/2226-3594-2022-59-05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a finite-dimensional Euclidean space, the problem of pursuit by a group of pursuers of two evaders described by a system of the form $$\\\\dot z_{ij} = u_i - v,\\\\quad u_i, v \\\\in V $$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is unit ball centered at zero, target sets are the origin. The goal of the pursuers' group is to capture at least one evader by two pursuers or to capture two evaders. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.\",\"PeriodicalId\":42053,\"journal\":{\"name\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.35634/2226-3594-2022-59-05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/2226-3594-2022-59-05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在有限维欧几里得空间中,考虑了由形式为$$\dot z_{ij} = u_i - v,\quad u_i, v \in V $$的系统描述的两个逃避者的一组追逐者的追逐问题。假设所有逃避者使用相同的控制。追捕者根据关于逃避者的初始位置和控制历史的信息使用对抗策略。容许控制的集合$V$是以零为中心的单位球,目标集合是原点。追捕者组的目标是被两个追捕者捕获至少一个逃避者或捕获两个逃避者。在初始位置和博弈参数方面,得到了捕获的充分条件。在本研究中,采用函数解析法作为基本方法,可以在一定保证时间内得到逼近问题可解的充分条件。
On one simple pursuit problem of two rigidly coordinated evaders
In a finite-dimensional Euclidean space, the problem of pursuit by a group of pursuers of two evaders described by a system of the form $$\dot z_{ij} = u_i - v,\quad u_i, v \in V $$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is unit ball centered at zero, target sets are the origin. The goal of the pursuers' group is to capture at least one evader by two pursuers or to capture two evaders. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.