On the Theory of Positional Differential Games for Neutral-Type Systems

For a dynamical system whose motion is described by neutral-type differential equations in Hale’s form, we consider a minimax–maximin differential game with a quality index evaluating the motion history realized up to the terminal time. The control actions of the players are subject to geometric con...

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Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 309; no. Suppl 1; pp. S83 - S92
Main Authors Lukoyanov, N. Yu, Plaksin, A. R.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2020
Springer Nature B.V
Subjects
Differential equations
Differential games
Game theory
Geometric constraints
Mathematics
Mathematics and Statistics
Minimax technique
Saddle points
control theory
neutral-type systems
differential games
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Summary:For a dynamical system whose motion is described by neutral-type differential equations in Hale’s form, we consider a minimax–maximin differential game with a quality index evaluating the motion history realized up to the terminal time. The control actions of the players are subject to geometric constraints. The game is formalized in classes of pure positional strategies with a memory of the motion history. It is proved that the game has a value and a saddle point. The proof is based on the choice of an appropriate Lyapunov–Krasovskii functional for the construction of control strategies by the method of an extremal shift to accompanying points.
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SourceType-Conference Papers & Proceedings-1
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ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543820040100