On Some Pursuit Differential Game Problem in a Hilbert Space

Jamilu Adamu; Aminu Sulaiman Halliru; Bala Ma’aji Abdulhamid

doi:10.46481/jnsps.2022.379

Authors

Jamilu Adamu
[email protected]

Department of Mathematics, Federal University, Gashua, Nigeria
Aminu Sulaiman Halliru
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
Bala Ma’aji Abdulhamid
Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.

Keywords:

Differential Game. pursuers. Evader.Integral constraint.Geometric constraint. Hilbert space.

Abstract

Abstract We study pursuit differential game problem in which a countable number of pursuers chase one evader. The problem is formulated in a Hilbert space l₂ with pursuers’ motions described by nth order differential equations and that of the evader by mth order differential equation. The control functions of the pursuers and evader are subject to integral and geometric constraints respectively.Duration of the game is denoted by the positive number?. Pursuit is said to be completed if there exist strategies uj of the pursuers Pj such that for any admissible control v(·) of the evader E the inequality ky(?) ? xj (?)k ? rj is satisfied for some j ? {1, 2, . . .}. In this paper, sufficient condition for completion of pursuit were obtained and also strategies of the pursuers that ensure completion of pursuit are constructed.

Dimensions

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