Pursuit differential game problem with integral and geometric constraints.

Jamilu Adamu,Bala Ma’Aji Abdulhamid,Aminu Sulaiman Halliru

doi:10.46481/jnsps.2022.379

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.

Highlights

A considerable amount of literature on differential game problem in which finite number of pursuers chase one evader in the Hilbert space l2, control function of players subjected to either geometric, integral or both constraints has been published
Adamu et al [1], studied pursuit-evasion differential game problem in a Hilbert space l2, in which motions of pursuers and evader are described by first and second order differential equations respectively. Control functions of both the pursuers and evader are subject to integral constrains
We found the sufficient condition of completion of pur- missible control v(·) of the evader E, the system (1)-(2) has a suit in l-catch sense

Summary

Introduction

A considerable amount of literature on differential game problem in which finite number of pursuers chase one evader in the Hilbert space l2, control function of players subjected to either geometric, integral or both constraints has been published. In many studies of differential game problems, motions of the two players (i.e. pursuer and evader) are explicitly stated and are considered to be differential equations of the same order. Adamu et al [1], studied pursuit-evasion differential game problem in a Hilbert space l2, in which motions of pursuers and evader are described by first and second order differential equations respectively. Control functions of both the pursuers and evader are subject to integral constrains. Strategy of pursuers were constructed sufficient to complete the pursuit from any initial position

Differential game formulation

MAIN RESULT

Conclusion