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Tr. Mat. Inst. Steklova, 2019, Volume 304, Pages 309–325 (Mi tm3977)  

The Programmed Iteration Method in a Game Problem of Realizing Trajectories in a Function Set

A. G. Chentsovab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia

Abstract: We consider a differential game in which one of the players tries to keep a trajectory within a given set of vector functions on a finite time interval; the goal of the second player is opposite. To construct the set of successful solvability in this problem, which is defined by the functional target set, we apply the programmed iteration method. The essence of the method lies in a universal game problem of programmed control that depends on parameters characterizing the constraints on the initial fragments of trajectories. As admissible control procedures, we use multivalued quasistrategies (regarding a conflict-controlled system, it is assumed that the conditions of generalized uniqueness and uniform boundedness of programmed motions are satisfied).

DOI: https://doi.org/10.4213/tm3977

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 292–308

Bibliographic databases:

UDC: 517.9
Received: July 29, 2018
Revised: July 29, 2018
Accepted: December 11, 2018

Citation: A. G. Chentsov, “The Programmed Iteration Method in a Game Problem of Realizing Trajectories in a Function Set”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 309–325; Proc. Steklov Inst. Math., 304 (2019), 292–308

Citation in format AMSBIB
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\by A.~G.~Chentsov
\paper The Programmed Iteration Method in a Game Problem of Realizing Trajectories in a Function Set
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 309--325
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3977}
\crossref{https://doi.org/10.4213/tm3977}
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\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 304
\pages 292--308
\crossref{https://doi.org/10.1134/S008154381901022X}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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