Pursuit differential game problem with integral and geometric constraints.

Journal of Nigerian Society of Physical Sciences

Bala Ma’aji Abdulhamid¹  Aminu Sulaiman Halliru²  Jamilu Adamu³ 

[1] Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.;Department of Mathematical Sciences, Bayero University, Kano, Nigeria;Department of Mathematics, Federal University, Gashua, Nigeria;

关键词: Differential Game. pursuers. Evader.Integral constraint.Geometric constraint. Hilbert space.;   

DOI  :  10.46481/jnsps.2022.379

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown