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.
 

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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

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