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A linear differential game on a plane with a minimum-type functional

โœ Scribed by A.R. Akhmetzhanov; A.A. Melikyan

Book ID
104020521
Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
453 KB
Volume
71
Category
Article
ISSN
0021-8928

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โœฆ Synopsis

A differential game on a plane with a functional in the form of the minimum, with respect to time, of a certain prescribed phase vector function (quality function) is considered. It is proved that the game value is constant outside a certain bounded region, consisting of two parts. In the first subregion, the value is equal to the quality function, and in the second it satisfies Bellman's equation. For the constant-value region, where the players' optimum strategies are not unique, single-valued guaranteeing players' strategies are proposed. The results of a numerical investigation of the problem are presented.

๐Ÿ“œ SIMILAR VOLUMES

Linear functional differential equations
Linear functional differential equations with Property A
โœ M.K. Grammatikopulos; R. Koplatadze; G. Kvinikadze ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 165 KB

In the paper the general linear functional differential equation with several distributed deviations is considered. Sufficient conditions for the equation to have Property A (see Definition 1.2 below) are established. The obtained results are new even for Eq. (1.4).