# Simple motion pursuit differential game problem of many players with integral and geometric constraints on controls function.

## Keywords:

Differential game, pursuer, evader, geometric constraint, integral constraint, Hilbert space## Abstract

We study a simple motion pursuit differential game of many pursuers and one evader in a Hilbert space $l_{2}$. The control functions of the pursuers and evader are subject to integral and geometric constraints respectively. Duration of the game is denoted by positive number $\theta $. Pursuit is said to be completed if there exist strategies $u_{j}$ of the pursuers $P_{j}$ such that for any admissible control $v(\cdot)$ of the evader $E$ the inequality $\|y(\tau)-x_{j}(\tau)\|\leq l_{j}$ is satisfied for some $ j\in \{1,2, \dots\}$ and some time $\tau$. In this paper, sufficient conditions for completion of pursuit were obtained. Consequently strategies of the pursuers that ensure completion of pursuit are constructed.

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## Published

## How to Cite

*Journal of the Nigerian Society of Physical Sciences*,

*3*(1), 12–16. https://doi.org/10.46481/jnsps.2021.148