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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 4, Pages 146–166 (Mi timm433)  
This article is cited in 8 scientific papers (total in 9 papers)

An approach-evasion differential game: Stochastic guide

N. N. Krasovskii, A. N. Kotel'nikova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (299 kB) Citations (9)
References:
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Abstract: A positional differential game of the approach-evasion of a conflict-controlled motion and a goal set within a given set is considered. Use is made of a solution of the associated boundary-value problem for a parabolic equation degenerating as the diffusion term vanishes to a Hamilton–Jacobi type equation, which is typical for techniques in the theory of differential games. Based on this, a control scheme with a stochastic guide is developed.
Keywords: approach-evasion alternative, strategy, probabilistic process, Ito equation, Lyapunov function.
Received: 15.05.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 269, Issue 1, Pages S191–S213
DOI: https://doi.org/10.1134/S0081543810060167
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: N. N. Krasovskii, A. N. Kotel'nikova, “An approach-evasion differential game: Stochastic guide”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 146–166; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S191–S213
Citation in format AMSBIB
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\by N.~N.~Krasovskii, A.~N.~Kotel'nikova
\paper An approach-evasion differential game: Stochastic guide
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 146--166
\mathnet{http://mi.mathnet.ru/timm433}
\elib{https://elibrary.ru/item.asp?id=12952762}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S191--S213
\crossref{https://doi.org/10.1134/S0081543810060167}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962360309}
Linking options:
  • https://www.mathnet.ru/eng/timm433
  • https://www.mathnet.ru/eng/timm/v15/i4/p146
    • This publication is cited in the following 9 articles:
    1. Olga Yufereva, “Approximate Capture in Gromov–Hausdorff Close Spaces”, Dyn Games Appl, 12:4 (2022), 1376  crossref
    2. D. V. Khlopin, “Differential Game with Discrete Stopping Time”, Autom Remote Control, 83:4 (2022), 649  crossref
    3. Dmitrii V. Khlopin, “Differentsialnaya igra s diskretnym momentom ostanovki”, MTIP, 13:4 (2021), 93–128  mathnet
    4. Yu. V. Averboukh, “Approximation of value function of differential game with minimal cost”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:4 (2021), 536–561  mathnet  crossref
    5. Averboukh Yu., “Approximate Public-Signal Correlated Equilibria For Nonzero-Sum Differential Games”, SIAM J. Control Optim., 57:1 (2019), 743–772  crossref  isi
    6. Kolpakova E.A., “On Approximation of Multivalued Solution For Hamilton-Jacobi Equation”, IFAC PAPERSONLINE, 51:32 (2018), 805–809  crossref  isi
    7. Averboukh Yu., “Extremal Shift Rule For Continuous-Time Zero-Sum Markov Games”, Dyn. Games Appl., 7:1 (2017), 1–20  crossref  mathscinet  zmath  isi  scopus
    8. “Nikolai Nikolaevich Krasovskii (on the occasion of his 90th birthday)”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 1–21  mathnet  crossref  mathscinet  isi
    9. N. N. Krasovskii, A. N. Kotel'nikova, “Stochastic control in a determinate differential pursuit–evasion game”, Autom. Remote Control, 72:2 (2011), 305–322  mathnet  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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