Abstract:
The stability property in a game problem of the approach of a conflict-controlled system to a goal set at a fixed terminal moment is investigated. The notion of a stability defect is introduced for sets in the space of game positions.
Citation:
V. N. Ushakov, Ya. A. Latushkin, “The stability defect of sets in game control problems”, Control, stability, and inverse problems of dynamics, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 2, 2006, 178–194; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S198–S215
\Bibitem{UshLat06}
\by V.~N.~Ushakov, Ya.~A.~Latushkin
\paper The stability defect of sets in game control problems
\inbook Control, stability, and inverse problems of dynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 2
\pages 178--194
\mathnet{http://mi.mathnet.ru/timm162}
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\zmath{https://zbmath.org/?q=an:1125.49030}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 255
\issue , suppl. 2
\pages S198--S215
\crossref{https://doi.org/10.1134/S0081543806060162}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846990946}
Linking options:
https://www.mathnet.ru/eng/timm162
https://www.mathnet.ru/eng/timm/v12/i2/p178
This publication is cited in the following 23 articles:
Vladimir N. Ushakov, Aleksandr M. Tarasev, “Igrovaya zadacha sblizheniya nelineinoi upravlyaemoi sistemy”, MTIP, 15:2 (2023), 122–139
V. N. Ushakov, A. M. Tarasyev, “Game Problem of Target Approach for a Nonlinear Control System”, Dokl. Math., 108:S1 (2023), S42
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. Uspenskii, “Weak invariance of a cylindrical set with smooth boundary with respect to a control system”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 164–172
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
P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algoritmy nailuchshei approksimatsii ploskikh mnozhestv ob'edineniyami krugov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 4, 88–99
A. A. Usova, “Ob asimptoticheskikh svoistvakh optimalnykh reshenii i funktsii tseny v zadachakh optimalnogo upravleniya na beskonechnom gorizonte”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 1, 77–95
V. N. Ushakov, A. A. Uspenskii, “Defekt stabilnosti deformatsii maksimalnogo stabilnogo mosta dlya igrovoi zadachi sblizheniya s zamknutoi tselyu”, Izv. IMI UdGU, 2012, no. 1(39), 140–140
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
Aleksandr M. Tarasev, Anastasiya A. Usova, “Vliyanie parametrov proizvodstvennykh funktsii na ravnovesnoe reshenie i funktsiyu tseny zadachi optimalnogo upravleniya”, MTIP, 3:3 (2011), 85–115
Ushakov V.N., “On the stability property in a game-theoretic approach problem with fixed terminal time”, Differ. Equ., 47:7 (2011), 1046–1058
V. N. Ushakov, A. G. Malev, “On the question of the stability defect of sets in an approach game problem”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S229–S254
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