Abstract
In this paper, we study a differential game in which a finite or countable number of pursuers pursue a single evader. The control functions of players satisfy integral constraints. The period of the game, which is denoted as \(\zeta \), is determined. The farness between the evader and the closest pursuer when the game is finished is the payoff function of the game. In the paper, we introduce the value of the game and identify optimal strategies of the pursuers. A significant facet of this work is that there is no relation between the energy resource of any pursuer and that of the evader for completing pursuit.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blagodatskih AI, Petrov NN (2009) Conflict interaction controlled objects groups. Udmurt State University, Izhevsk (in Russian)
Ferrara M, Ibraimov G, Salimi M (2017) Pursuit-evasion game of many players with coordinate-wise integral constraints on a convex set in the plane. AAPP Atti della Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche Matematiche e Naturali 95(2):A6
Ibragimov G (2005) Optimal pursuit with countably many pursuers and one evader. Differ Equ 41(5):627–635
Ibragimov G, Salimi M (2009) Pursuit-evasion differential game with many inertial players. Math Probl Eng 2009:653723
Ibragimov G, Salimi M, Amini M (2012) Evasion from many pursuers in simple motion differential game with integral constraints. Eur J Oper Res 218:505–511
Ibragimov G, Norshakila AR, Kuchkarov A, Fudziah I (2015) Multi pursuer differential game of optimal approach with integral constraints on controls of players. Taiwan J Math 19(3):963–976
Isaacs R (1965) Differential games. Wiley, New York
Ivanov RP, Ledyaev YuS (1981) Optimality of pursuit time in differential game of several objects with simple motion. Proc Steklov Inst Math 158:93–104
Krasovskii NN (1985) Control of a dynamical system. Nauka, Moscow
Levchenkov AY, Pashkov AG (1990) Differential game of optimal approach of two inertial pursuers to a noninertial evader. J Optim Theory Appl 65(3):501–517
Pashkov AG, Terekhov SD (1983) On a game of optimal pursuit of one object by two objects. Prikl Mat Mekh 47(6):898–903
Petrosyan LA (1977) Differential pursuit games. Izdat Leningrad University, Leningrad
Petrov NN (1988) About one group pursuit problem with phase constraints. Prikl Mat Mekh 6:1060–1063
Pontryagin LS (2004) Selected works. MAKS Press, Moscow
Rikhsiev BB (1989) The differential games with simple motions. Fan, Tashkent
Rzymowski W (1986) Evasion along each trajectory in differential games with many pursuers. J Differ Equ 62(3):334–356
Salimi M (2018) A research contribution on an evasion problem. SeMA J 75(1):139–144
Salimi M, Ibragimov G, Siegmund S, Sharifi S (2016) On a fixed duration pursuit differential game with geometric and integral constraints. Dyn Games Appl 6(3):409–425
Subbotin AI, Chentsov AG (1981) Optimizatsiya garantii v zadachakh upravleniya (Optimization of guaranteed result in control problems). Nauka, Moscow
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Salimi, M., Ferrara, M. Differential game of optimal pursuit of one evader by many pursuers. Int J Game Theory 48, 481–490 (2019). https://doi.org/10.1007/s00182-018-0638-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-018-0638-6