Vol 5 . Paper 9

Pursuit Differential Game Problems Of L-Catch in A Hilbert Space

Yunusa Aliyu Hadejia, Sani Salisu, Idris Ahmed, Sani Musa

Keywords: Differential Games, Hilbert Space, l-catch, p-strategy, and Geometric constraints

Abstract

We propose some fixed duration pursuit differential game problems of l-catch in a Hilbert space. Players’ motion obey ordinary differential equations and the control functions of players are subjected to either integral or geometric constraints. Pursuit is said to be completed in l-catch sense if the distance between the players with conflicting goals is less than a fixed constant l. The problem of 𝑙-catch pursuit with four different combination of player’s constraints were considered and we obtained sufficient conditions for completion of pursuit in each case. Furthermore, we give examples to support our theoretical findings.