Pursuit and Evasion Differential Games in Hilbert Space

Abstract

We consider pursuit and evasion differential game problems described by an infinite system of differential equations with countably many Pursuers in Hilbert space. Integral constraints are imposed on the controls of players. In this paper an attempt has been made to solve an evasion problem under the condition that the total resource of the Pursuers is less then that of the Evader and a pursuit problem when the total resource of the Pursuers greater than that of the Evader. The strategy of the Evader is constructed.

A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$

“…Ibragimov and Risman [21] considered pursuit and evasion differential game described by (2) in a certain Hilbert space they introduced as 2 r with integral constraints on control functions of the players, where the space with inner product and norm defined by respectively, for a given fixed number r and monotonically increasing sequence of positive numbers { k } k∈ℕ . The evasion problem was studied on some disjoint subset (octants) of 2 r and solved with the assumption that the total resources of the pursuers is less than the evader's while the pursuit problem was solved in contrary to this assumption.…”

Evasion differential game of two evaders and one pursuer with integral constraints

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14]. More specifically, there were a few works on the related problem in the case of many pursuers and one evader.…”

“…Ibragimov and Risman [9] studied an evasion differential game of countably many pursuers and one evader governed by infinite systems of differential equations: …”

An evasion differential game problem on the plane

“…There are many publications from researches involving this type of differential game problem. Some of these publications include Azamov (1964), Chodun (1987), Ibragimov and Yusra (2012), Hasim(2012), Ibragimov et. al.…”

“…There are many om researches involving this type of differential game problem. Some of these publications (1987), Ibragimov (2012), Ibragimov and Hasim(2012) Ibragimov and Yusra (2012) studied evasion differential described by simple equations which involved many pursuer and one evader in the plane. Each coordinate of the control functions of the players is subjected to integral constraints.…”