Abstract:
A two-person differential game is considered. The game is described by the system of differential equations $\dot x = f(x, u) + g(x, v)$, where $x \in \mathbb R^k$, $u \in U$, $v \in V$. The pursuer's admissible control set is a finite subset of phase space. The evader's admissible control set is a compact subset of phase space. The pursuer's purpose is to capture the evader, viz. system translation to any given neighborhood of zero. Sufficient conditions for the solvability of a capture problem in the piecewise open-loop strategies class are obtained. In addition, it is proved that the capture time tends to zero with the initial position approaching to zero. It happens independent of the evader's actions.
Citation:
K. A. Shchelchkov, “A nonlinear pursuit problem with discrete control and incomplete information”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 111–118
\Bibitem{Shc18}
\by K.~A.~Shchelchkov
\paper A nonlinear pursuit problem with discrete control and incomplete information
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 111--118
\mathnet{http://mi.mathnet.ru/vuu624}
\crossref{https://doi.org/10.20537/vm180110}
\elib{https://elibrary.ru/item.asp?id=32697220}
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This publication is cited in the following 8 articles:
K. A. Shchelchkov, “On the Problem of Controlling a Nonlinear System
by a Discrete Control under Disturbance”, Diff Equat, 60:1 (2024), 127
K. A Shchelchkov, “O ZADAChE UPRAVLENIYa NELINEYNOY SISTEMOY POSREDSTVOM DISKRETNOGO UPRAVLENIYa V USLOVIYaKh VOZDEYSTVIYa POMEKhI”, Differencialʹnye uravneniâ, 60:1 (2024), 126
K. A. Shchelchkov, “Relative optimality in nonlinear differential games with discrete control”, Sb. Math., 214:9 (2023), 1337–1350
K. A. Shchelchkov, “One-Sided Capture in Nonlinear Differential Games”, Int. Game Theory Rev., 25:02 (2023)
Shchelchkov K., “Epsilon-Capture in Nonlinear Differential Games Described By System of Order Two”, Dyn. Games Appl., 12:2 (2022), 662–676
K. A. Shchelchkov, “Estimate of the Capture Time and Construction of the Pursuer's Strategy in a Nonlinear Two-Person Differential Game”, Diff Equat, 58:2 (2022), 264
A. A. Dubanov, T. V. Ausheev, “Geometric model of persecution by a group of one goal”, Iv International Scientific and Technical Conference Mechanical Science and Technology Update (Mstu-2020), Journal of Physics Conference Series, 1546, IOP Publishing Ltd, 2020, 012036
A. Ya. Narmanov, K. A. Schelchkov, “Zadacha ukloneniya v nelineinoi differentsialnoi igre s diskretnym upravleniem”, Izv. IMI UdGU, 52 (2018), 75–85
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