A differential game of pursuit for an infinite system of simple motion in the plane

Usman Waziri; Abdullahi Usman; Lawan Bulama Mohammed; Abubakar Abdullahi

doi:10.54117/gjpas.v1i2.41

Authors

Usman Waziri Department of Mathematical Sciences, Faculty of Science, Bauchi State University Gadau, Nigeria.
Abdullahi Usman Department of Mathematical Sciences, Faculty of Science, Bauchi State University Gadau, Nigeria.
Lawan Bulama Mohammed Department of Mathematical Sciences, Faculty of Science, Federal University Dutse, Nigeria.
Abubakar Abdullahi General Studies Unit, Gombe State Polytechnic, Bajoga, Nigeria.

DOI:

https://doi.org/10.54117/gjpas.v1i2.41

Keywords:

Differential Game, Pursuer, Evader, Integral Constraint, Geometric Constraint, Strategy

Abstract

In the present paper, we investigate a differential game of pursuit for an infinite system of simple motion in a plane. The control functions of the players satisfies both geometric and integral constraints respectively. In the plane, the game is assume to be completed if the state of the pursuer xk, k = 1, 2, ... is directly coincide with that of the evader yk, k = 1, 2, ..., i.e; xk(x ) = yk(x ), k = 1,2, ..., at some time x and the evader is tries to stop the incident. In addition to that the strategy of the pursuer with respect to geometric and integral constraints will be constructed. Moreover, a numerical example will be given to illustrate the result.

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