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

https://doi.org/10.46481/jnsps.2021.148

Authors

  • Jamilu Adamu Department of Mathematics, Federal University Gashua, Yobe, Nigeria
  • B. M. Abdulhamid Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.
  • D. T. Gbande Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
  • A. S. Halliru Department of Mathematical Sciences, Bayero University, Kano, Nigeria.

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.

Dimensions

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Published

2021-02-18

How to Cite

Adamu, J., B. M. Abdulhamid, D. T. Gbande, & A. S. Halliru. (2021). Simple motion pursuit differential game problem of many players with integral and geometric constraints on controls function . Journal of the Nigerian Society of Physical Sciences, 3(1), 12–16. https://doi.org/10.46481/jnsps.2021.148

Issue

Section

Original Research