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

Journal of Nigerian Society of Physical Sciences

B. M. Abdulhamid¹  A. S. Halliru²  D. T. Gbande²  Jamilu Adamu³ 

[1] Department of Mathematical Sciences, Abubakar Tafawa Balewa University, Bauchi, Nigeria.;Department of Mathematical Sciences, Bayero University, Kano, Nigeria.;Department of Mathematics, Federal University Gashua, Yobe, Nigeria;

关键词: Differential game;    pursuer;    evader;    geometric constraint;    integral constraint;    Hilbert space;   

DOI  :  10.46481/jnsps.2021.148

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown