一类考虑滑动摩擦力影响的追逃博弈问题  

A class of pursuit-evasion game problems considering the influence of sliding friction

作　　者：侯敏 于洋 戴照鹏 敬鲁晶 高红伟 HOU Min;YU Yang;DAI Zhaopeng;JING Lujing;GAO Hongwei(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Shandong,China;Institute of Applied Mathematics of Shandong,Qingdao 266071,Shandong,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071 [2]山东省应用数学研究所,山东青岛266071

出　　处：《运筹学学报(中英文)》2025年第1期114-126,共13页Operations Research Transactions

基　　金：国家自然科学基金(Nos.72171126,11872220);青岛大学“系统科学+”联合攻关项目(No.XT2024301)。

摘　　要：本文以追逃博弈问题的经典模型之一——“homicidal chauffeur”博弈为基础,考察汽车转弯时受滑动摩擦力影响的博弈问题的捕获区域。经典“homicidal chauffeur”博弈是基于足够粗糙的地面这一理想假设对汽车转弯时的速度进行处理的。然而在现实运动中,地面粗糙程度不同会对转弯时汽车的速度造成不同的影响。本文建立模型对追逃过程中汽车速度给出全新的刻画,求解最优策略,分析与经典“homicidal chauffeur”博弈相比捕获区域的变化并阐述原因,主要结论可用于陆地追逃、空战格斗等现实场景。Based on the homicidal chauffeur game,one of the classic models of the pursuit-evasion game problem,this paper investigates the capture area of the game problem that is affected by the sliding friction when the car turns.The classic homicidal chauffeur game deals with the speed of a car turning a corner based on the ideal assumption of a sufficiently rough ground.However,in real sports,different ground roughness will have different effects on the speed of the car when cornering.In this paper,a model is established to give a new description of the speed of the car in the process of chasing and fleeing,to solve the optimal strategy,to analyze the changes in the capture area compared with the classic homicidal chauffeur game and to explain the reasons.The main conclusions can be used for land pursuit,space combat and other realistic scenes.

关 键 词："homicidal chauffeur"博弈 追逃微分博弈 最优策略 界栅 

分 类 号：O225[理学—运筹学与控制论]