Abstract:
Pontryagin's classical nonstationary example with many participants and phase constraints on the evader's states with equal dynamic and inertia capabilities of the players is considered. The case of a simple motion is considered separately. Solvability conditions for problems of pursuit and evasion are obtained.
Keywords:
group pursuit, nonstationary problem, Pontryagin's example, phase constraints.
Citation:
A. S. Bannikov, N. N. Petrov, “On a nonstationary problem of group pursuit”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 40–51; Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S41–S52
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\paper On a~nonstationary problem of group pursuit
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\pages 40--51
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
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\pages S41--S52
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Linking options:
https://www.mathnet.ru/eng/timm526
https://www.mathnet.ru/eng/timm/v16/i1/p40
This publication is cited in the following 39 articles:
Alexander Dubanov, Lecture Notes in Networks and Systems, 909, Software Engineering Methods in Systems and Network Systems, 2024, 451
N. N. Petrov, N. A. Solov'eva, “Multiple Capture of a Given Number of Evaders in L. S. Pontryagin's Recurrent Example”, J Math Sci, 2024
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
B. T. Samatov, A. Kh. Akbarov, B. I. Zhuraev, “Pursuit–evasion differential games with Gr-constraints on controls”, Izv. IMI UdGU, 59 (2022), 67–84
Dubanov Alexander, Lecture Notes in Networks and Systems, 501, Software Engineering Perspectives in Systems, 2022, 262
B. T. Samatov, M. A. Horilov, A. Ah. Akbarov, “Differential Game: "Life Line" for Non-Stationary Geometric Constraints On Controls”, Lobachevskii J Math, 43:1 (2022), 237
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
Ibragimov G., Ferrara M., Ruziboev M., Pansera B.A., “Linear Evasion Differential Game of One Evader and Several Pursuers With Integral Constraints”, Int. J. Game Theory, 50:3 (2021), 729–750
N. N. Petrov, N. A. Soloveva, “Mnogokratnaya poimka zadannogo chisla ubegayuschikh v rekurrentnom primere L. S. Pontryagina”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 108–115
Dubanov A.A., Ausheev V T., Iv International Scientific and Technical Conference Mechanical Science and Technology Update (Mstu-2020), Journal of Physics Conference Series, 1546, IOP Publishing Ltd, 2020
Nikolai N. Petrov, Nadezhda A. Solov'eva, “Capture of Given Number of Evaders in Pontryagin's Nonstationary Example”, Dyn Games Appl, 9:3 (2019), 614
G. Ibragimov, M. Ferrara, A. Kuchkarov, B. A. Pansera, “Simple Motion Evasion Differential Game of Many Pursuers and Evaders With Integral Constraints”, Dyn. Games Appl., 8:2 (2018), 352–378
A. Ya. Narmanov, K. A. Schelchkov, “Zadacha ukloneniya v nelineinoi differentsialnoi igre s diskretnym upravleniem”, Izv. IMI UdGU, 52 (2018), 75–85
Nikolay Petrov, 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy's Conference) (STAB), 2018, 1
N. N. Petrov, N. A. Soloveva, “Mnogokratnaya poimka ubegayuschego v lineinykh rekurrentnykh differentsialnykh igrakh”, Tr. IMM UrO RAN, 23:1 (2017), 212–218
N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recurrent example”, Autom. Remote Control, 77:5 (2016), 855–861
M. N. Vinogradova, “O poimke dvukh ubegayuschikh v odnoi nestatsionarnoi zadache gruppovogo presledovaniya s fazovymi ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 12–20
N. N. Petrov, N. A. Solov'eva, “Multiple capture in Pontryagin's recursive example with phase constraints”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 174–182
Citation in format AMSBIB
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