On Some Pursuit Differential Game Problem in a Hilbert Space

Authors

  • Jamilu Adamu 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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Published

2022-02-27

How to Cite

On Some Pursuit Differential Game Problem in a Hilbert Space. (2022). Journal of the Nigerian Society of Physical Sciences, 4(1), 83-87. https://doi.org/10.46481/jnsps.2022.379

Issue

Volume 4, Issue 1, February 2022

Section

Original Research
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How to Cite

On Some Pursuit Differential Game Problem in a Hilbert Space. (2022). Journal of the Nigerian Society of Physical Sciences, 4(1), 83-87. https://doi.org/10.46481/jnsps.2022.379