Abstract:
The stability property is studied in a game problem of the approach of a conflict-controlled system to a target set at a fixed termination time. The notion of the stability defect of sets in the space of game positions is investigated.
Keywords:
approach game problem, control, conflict-controlled system, stable bridge, Hamiltonian.
Citation:
V. N. Ushakov, A. G. Malev, “On the question of the stability defect of sets in an approach game problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 199–222; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S229–S254
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\by V.~N.~Ushakov, A.~G.~Malev
\paper On the question of the stability defect of sets in an approach game problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 199--222
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 272
\issue , suppl. 1
\pages S229--S254
\crossref{https://doi.org/10.1134/S0081543811020179}
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Linking options:
https://www.mathnet.ru/eng/timm538
https://www.mathnet.ru/eng/timm/v16/i1/p199
This publication is cited in the following 22 articles:
V. N. Ushakov, V. I. Ukhobotov, A. E. Lipin, “An Addition to the Definition of a Stable Bridge and an Approximating System of Sets in Differential Games”, Proc. Steklov Inst. Math., 304 (2019), 268–280
Ushakov V.N. Malev A.G., “Stability Defect Estimation For Sets in a Game Approach Problem At a Fixed Moment of Time”, Dokl. Math., 100:3 (2019), 533–537
Vladimir N. Ushakov, Studies in Systems, Decision and Control, 203, Advanced Control Techniques in Complex Engineering Systems: Theory and Applications, 2019, 83
A. A. Chikrii, “Verkhnyaya i nizhnyaya razreshayuschie funktsii v igrovykh zadachakh dinamiki”, Tr. IMM UrO RAN, 23:1 (2017), 293–305
L. I. Rodina, A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemoi sistemy”, Izv. IMI UdGU, 2016, no. 1(47), 44–53
V. N. Ushakov, P. D. Lebedev, “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 225–237
V.N. Ushakov, A.G. Malev, “One estimation of the stability defect of sets in an approach game problem**This work was supported by the Russian Science Foundation (project no. 15-11-10018).”, IFAC-PapersOnLine, 48:25 (2015), 162
A. G. Malev, “K voprosu ob otsenke defekta stabilnosti mnozhestv v igrovoi zadache o sblizhenii”, Tr. IMM UrO RAN, 19, no. 1, 2013, 205–216
L. I. Rodina, “Estimation of statistical characteristics of attainability sets of controllable systems”, Russian Math. (Iz. VUZ), 57:11 (2013), 17–27
V. N. Ushakov, A. N. Kotel'nikova, A. G. Malev, “On estimation of the stability defect of the sets with piecewise smooth border”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 185–201
L. I. Rodina, “Statisticheskie kharakteristiki mnozhestva dostizhimosti i periodicheskie protsessy upravlyaemykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 2, 34–43
L. I. Rodina, “Invariantnye i statisticheski slabo invariantnye mnozhestva upravlyaemykh sistem”, Izv. IMI UdGU, 2012, no. 2(40), 3–164
V. N. Ushakov, P. D. Lebedev, A. R. Matviychuk, A. G. Malev, “Differential games with fixed terminal time and estimation of the instability degree of sets in these games”, Proc. Steklov Inst. Math., 277 (2012), 266–277
V. N. Ushakov, A. A. Zimovets, “K voprosu o slaboi invariantnosti mnozhestv otnositelno differentsialnogo vklyucheniya, porozhdennogo upravlyaemoi sistemoi”, Tr. IMM UrO RAN, 18, no. 4, 2012, 271–285
V. N. Ushakov, A. A. Uspenskii, A. G. Malev, “Estimate of the stability defect for a positional absorption set subjected to discriminant transformations”, Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 113–129
V. N. Ushakov, A. A. Zimovets, “Defekt invariantnosti mnozhestv otnositelno differentsialnogo vklyucheniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2011, no. 2, 98–111
Ushakov V.N., “On the stability property in a game-theoretic approach problem with fixed terminal time”, Differ. Equ., 47:7 (2011), 1046–1058
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