Abstract:
We consider Pontryagin's generalized nonstationary example with identical dynamic and inertial capabilities of the players and state constraints on the evader's states. The boundary of the phase constraints is not a “death line” for the evader. The set of admissible controls is a ball centered at the origin, and the terminal sets are the origin. We obtain sufficient conditions for a multiple capture of one evader by a group of pursuers in the case when some functions corresponding to the initial data and parameters of the game are recursive.
Keywords:pursuer, evader, phase restrictions, Pontryagin's example, group pursuit.
Citation:
N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recursive example with phase constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 178–186; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 174–182
\Bibitem{PetSol15}
\by N.~N.~Petrov, N.~A.~Solov'eva
\paper Multiple capture in Pontryagin's recursive example with phase constraints
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 178--186
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
\issue , suppl. 1
\pages 174--182
\crossref{https://doi.org/10.1134/S0081543816050163}
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Linking options:
https://www.mathnet.ru/eng/timm1180
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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
Alena I. Machtakova, Nikolai N. Petrov, “Matrix resolving functions in the linear group pursuit problem with fractional derivatives”, Ural Math. J., 8:1 (2022), 76–89
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
N. N. Petrov, N. A. Solov'eva, “Multiple capture of given number of evaders in linear recurrent differential games”, J. Optim. Theory Appl., 182:1, SI (2019), 417–429
N. N. Petrov, “Group pursuit problem in a differential game with fractional derivatives, state constraints, and simple matrix”, Differ. Equ., 55:6 (2019), 841–848
N. N. Petrov, “A multiple capture in a group pursuit problem with fractional derivatives”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S150–S157
N. N. Petrov, A. Ya. Narmanov, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v zadache prostogo presledovaniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:2 (2018), 193–198
A. Ya. Narmanov, K. A. Schelchkov, “Zadacha ukloneniya v nelineinoi differentsialnoi igre s diskretnym upravleniem”, Izv. IMI UdGU, 52 (2018), 75–85
N. N. Petrov, N. A. Soloveva, “Mnogokratnaya poimka ubegayuschego v lineinykh rekurrentnykh differentsialnykh igrakh”, Tr. IMM UrO RAN, 23:1 (2017), 212–218