N.Yu. Lukoyanov, A.R. Plaksin. To the theory of positional differential games for neutral-type systems ... P. 118-128

For a dynamic 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 in the construction of control strategies by the method of an extremal shift to accompanying points.

Keywords: neutral-type systems, control theory, differential games

Received April 16, 2019

Revised May 14, 2019

Accepted May 20, 2019

Funding Agency: This work was supported by the Russian President’s Grant for Young Russian Scientists no. MK-3566.2019.1.

Nikolai Yur’evich Lukoyanov, Dr. Phys.-Math. Sci., Corresponding Member of RAS, Prof., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620083 Russia,
e-mail: nyul@imm.uran.ru

Anton Romanovich Plaksin, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620083 Russia, e-mail: a.r.plaksin@gmail.com

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Cite this article as: N.Yu. Lukoyanov, A.R. Plaksin. To the theory of positional differential games for neutral-type systems, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 118–128.