On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints

Abstract

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to geometric constraints and the controls of the other pursuers and the evader are subject to integral constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game.2010 Mathematics Subject Classification. 91A23.

Differential game of optimal pursuit of one evader by many pursuers

“…Finding the value of the game and identifying optimal strategies of players are two interesting subjects in the study of pursuit evasion problems. Such issues for many players with a variety of constraints have been studied in Ferrara et al (2017), Ibragimov (2005), Ibragimov et al (2012Ibragimov et al ( , 2015, Ibragimov and Salimi (2009), Ivanov and Ledyaev (1981) and Salimi et al (2016). Ibragimov et al (2015) study an inertial pursuit evasion game with a finite or countable number of pursuers and one evader in Hilbert space 2 .…”

Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex

“…Differential games of many players with integral constraints on the control functions of the players are also of increasing interest. For example, the works [23][24][25][26][27][28] dealt with the evasion differential games of many pursuers.…”

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

“…Finding the value of the game and identifying optimal strategies of players are two interesting subjects in the study of pursuit evasion problems. Such issues for many players with a variety of constraints have been studied in [6], [8], [9], [10], [12], [13], [25], [26] and [27].…”