Open AccessPursuit differential game problem with integral and geometric constraints.
Author(s) -
Jamilu Adamu,
Aminu Sulaiman Halliru,
Bala Ma’aji Abdulhamid
Publication year - 2022
Publication title -
journal of the nigerian society of physical sciences
Language(s) - English
Resource type - Journals
ISSN - 2714-4704
DOI - 10.46481/jnsps.2022.379
Subject(s) - differential game , countable set , mathematics , differential (mechanical device) , differential equation , hilbert space , order (exchange) , space (punctuation) , mathematical analysis , mathematical optimization , combinatorics , computer science , finance , engineering , economics , aerospace engineering , operating system
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.