On Control and Differential Game Problems in Hilbert Space

F. Allahabi¹

1. Department of Mathematics, Faculty of Applied Science, Thamar University, Thamar, Yemen.

Correspondence should be addressed to: fateh.allahabi@tu.edu.ye, Tel.: +967-7717-34514.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.65-69, Apr-2020

Online published on Apr 30, 2020

Copyright © F. Allahabi . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

246 Views    277 Downloads    109 Downloads

Abstract :
In this paper we investigate a control and pursuit game problems of an infinite system of first order differential equations. This work suggest a new approach to construct the control functions of pursuers in Hilbert space. First, in the control problem, we obtain the sufficient conditions for possibility to bring the control system from the initial point to the origin in finite time. Second, in the pursuit game problem with geometric and integral constraints on the controls of players, we established the sufficient conditions for which pursuit game is possible to complete the pursuit.

Key-Words / Index Term :
Differential game, pursuit game, control, admissibility, pursuit time

References :
[1] O. A. Ladyzhenskaya, “Boundary-Value Problems of Matahematical Physics,” [in Russian], Nauka, Moscow, 1973.
[2] F.L. Chernous’ko, “Bounded Controls in Systems with Distributed Parameters,” Prikl. Mat. Mekh, Vol. 56, Issue.5, pp. 810-826, 1992.
[3] F.L. Chernous’ko, “On the construction of a bounded control in oscillatory systems,” Journal of Applied Mathematics and Mechanics, Vol.52, Issue.4, pp. 426-433, 1988.
[4] F.L. Chernous’ko, “Decomposition and suboptimal control in dynamical systems,” Journal of Applied Mathematics and Mechanics, Vol.54, Issue.6, pp. 727-734, 1990.
[5] N. Yu. Satimov, M. Tukhtasinov, “On some game problems for rst-order controlled evolution equations,” Differential Equations, Vol.41. No.8, pp.1169-1177, 2005.
[6] N. Yu. Satimov, M. Tukhtasinov, “Game Problems on a Fixed Interval in Controlled First-Order Evolution Equations,” Mathematical Notes, Vol.80, No.4, pp. 578-589, 2006.
[7] G.I. Ibragimov, F. Allahabi, A. Kuchkarov “A pursuit problem in an infinite system of second-order differential equations,” Ukr. Math. J, Vol.65, No.8, pp.1203-1216, 2014
[8] M. Tukhtasinov, M. Sh. Mamatov, “On Pursuit Problems in Controlled Distributed Systems,” Mathematical Notes, Vol.84, No.2, pp.256–262, 2008.
[9] G.I. Ibragimov, A. Akhmedov, Puteri Nur Izzati, N. Abdul
Manaf, “Pursuit Differential Game Described by infinite First Order 2-Systems of Differential Equations,” Malaysian Journal of Mathematical Sciences. Vol.11, Issue.2, pp.181-190, 2017.
[10] F. Allahabi, , M. Abdulkawi Mahiub “A Problem of Pursuit Game with Various Constraints on Controls of Players,” International Journal of Partial Differential Equations and Applications, Vol.6, No.1, pp.13-17, 2019.
[11] Arti Kaushik, “Some Problems of Non Homogeneous Differential Equation of First Order and First Degree, Solved By the Method of Homogeneous Differential Equation of First Order and First Degree,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, No.14, pp.40-43, 2019.
[12] Arti Kaushik, “Numerical Study of a Steady State Two Dimensions Heat equation using TDMA Technique,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.4, No.1, pp.6-11, 2017.