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@article{IIMI_2023_61_a5, author = {B. T. Samatov and U. B. Soyibboev}, title = {Differential game with {\textquotedblleft}lifeline{\textquotedblright} for {Pontryagin's} control example}, journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta}, pages = {94--113}, publisher = {mathdoc}, volume = {61}, year = {2023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IIMI_2023_61_a5/} }
TY - JOUR AU - B. T. Samatov AU - U. B. Soyibboev TI - Differential game with “lifeline” for Pontryagin's control example JO - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta PY - 2023 SP - 94 EP - 113 VL - 61 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IIMI_2023_61_a5/ LA - en ID - IIMI_2023_61_a5 ER -
%0 Journal Article %A B. T. Samatov %A U. B. Soyibboev %T Differential game with “lifeline” for Pontryagin's control example %J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta %D 2023 %P 94-113 %V 61 %I mathdoc %U http://geodesic.mathdoc.fr/item/IIMI_2023_61_a5/ %G en %F IIMI_2023_61_a5
B. T. Samatov; U. B. Soyibboev. Differential game with “lifeline” for Pontryagin's control example. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 61 (2023), pp. 94-113. http://geodesic.mathdoc.fr/item/IIMI_2023_61_a5/
[1] Isaacs R., Differential games, John Wiley and Sons, New York, 1965 | MR | Zbl
[2] Pontryagin L.S., Selected works, MAKS Press, Moscow, 2004
[3] Krasovskii N.N., Control by dynamical system. The minimum problem of a guaranteed result, Nauka, Moscow, 1985 | MR | Zbl
[4] Pshenichnyi B.N., “Simple pursuit by several objects”, Cybernetics, 12:3 (1976), 484–485 | DOI | MR
[5] Petrosjan L.A., Differential games of pursuit, World Scientific Publishing, Singapore, 1993 | DOI | MR | Zbl
[6] Friedman A., Differential games, Wiley, New York, 1971 | MR | Zbl
[7] Fleming W.H., “The convergence problem for differential games, II”, Advances in game theory, 1964, 195–210 | DOI | MR | Zbl
[8] Bercovitz L.D., “Differential games of generalized pursuit and evasion”, SIAM Journal on Control and Optimization, 24:3 (1986), 361–373 | DOI | MR
[9] Chikrii A., Conflict-controlled processes, Springer, Dordrecht, 1997 | DOI | MR
[10] Subbotin A.I., “Generalization of the main equation of differential game theory”, Journal of Optimization Theory and Applications, 43:1 (1984), 103–133 | DOI | MR | Zbl
[11] Satimov N.Yu., Methods of solving pursuit problems in the theory of differential games, National University of Uzbekistan, Tashkent, 2019
[12] Petrov N.N., ““Soft” capture in Pontryagin's example with many participants”, Journal of Applied Mathematics and Mechanics, 67:5 (2003), 671–680 | DOI | MR | Zbl
[13] Azamov A., “On the quality problem for simple pursuit games with constraint”, Serdica. Bulgariacae mathematicae publicationes, 12:1 (1986), 38–43 (in Russian) http://www.math.bas.bg/serdica/1986/1986-038-043.pdf | MR | Zbl
[14] Azamov A.A., Samatov B.T., “The $\Pi$-strategy: Analogies and applications”, Contributions to Game Theory and Management, 4 (2011), 33–46 | MR | Zbl
[15] Azamov A.A., Samatov B.T., $\Pi$-strategy, National University of Uzbekistan, Tashkent, 2000
[16] Samatov B.T., “Problems of group pursuit with integral constraints on controls of the players. I”, Cybernetics and Systems Analysis, 49:5 (2013), 756–767 | DOI | MR | Zbl
[17] Petrov N.N., “Simple group pursuit subject to phase constraints and data delay”, Journal of Computer and Systems Sciences International, 57:1 (2018), 37–42 | DOI | MR | Zbl
[18] Petrov N.N., Narmanov A.Ya., “Multiple capture of a given number of evaders in the problem of a simple pursuit”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 28:2 (2018), 193–198 (in Russian) | DOI | MR | Zbl
[19] Grigorenko N.L., Mathematical methods for controlling several dynamic processes, Moscow State University, Moscow, 1990
[20] Vagin D.A., Petrov N.N., “Pursuit of a group of evaders in the Pontryagin example”, Journal of Applied Mathematics and Mechanics, 68:4 (2004), 555–560 | DOI | MR | Zbl
[21] Kornev D.V., Lukoyanov N.Yu., “On a minimax control problem for a positional functional under geometric and integral constraints on control actions”, Proceedings of the Steklov Institute of Mathematics, 293, suppl. 1 (2016), 85–100 | DOI | MR
[22] Ibragimov G., Ferrara M., Ruziboev M., Pansera B.A., “Linear evasion differential game of one evader and several pursuers with integral constraints”, International Journal of Game Theory, 50:3 (2021), 729–750 | DOI | MR | Zbl
[23] Ibragimov G.I., “The optimal pursuit problem reduced to an infinite system of differential equations”, Journal of Applied Mathematics and Mechanics, 77:5 (2013), 470–476 | DOI | MR | Zbl
[24] Samatov B.T., “On a pursuit-evasion problem under a linear change of the pursuer resource”, Siberian Advances in Mathematics, 23:4 (2013), 294–302 | DOI | MR | Zbl
[25] Samatov B.T., “The pursuit-evasion problem under integral-geometric constraints on pursuer controls”, Automation and Remote Control, 74:7 (2013), 1072–1081 | DOI | MR | Zbl
[26] Bannikov A.S., “Some non-stationary problems of group pursuit”, Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2013, no. 1(41), 3–46 (in Russian) | Zbl
[27] Bannikov A.S., Petrov N.N., “On a nonstationary problem of group pursuit”, Proceedings of the Steklov Institute of Mathematics, 271, suppl. 1 (2010), 41–52 | DOI | MR | Zbl
[28] Samatov B.T., Ibragimov G., Khodjibayeva I.V., “Pursuit-evasion differential games with the Grönwall type constraints on controls”, Ural Mathematical Journal, 6:2 (2020), 95-107 | DOI | MR | Zbl
[29] Yuldashev T.K., “Nonlinear optimal control of thermal processes in a nonlinear inverse problem”, Lobachevskii Journal of Mathematics, 41:1 (2020), 124–136 | DOI | MR | Zbl
[30] Vassilina G.K., “Optimal control problem of stochastic systems”, Lobachevskii Journal of Mathematics, 42:3 (2021), 641–648 | DOI | MR | Zbl
[31] Ushakov V.N., Ershov A.A., Ushakov A.V., Kuvshinov O.A., “Control system depending on a parameter”, Ural Mathematical Journal, 7:1 (2021), 120–159 | DOI | MR | Zbl
[32] Filippova T.F., “Estimates of reachable sets for systems with impulsive control, uncertainty and nonlinearity”, Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Ser. Matematika, 19 (2017), 205–216 (in Russian) | DOI | Zbl
[33] Munts N.V., Kumkov S.S., “Numerical method for solving time-optimal differential games with lifeline”, Matematicheskaya Teoriya Igr i Ee Prilozheniya, 10:3 (2018), 48–75 (in Russian) | Zbl
[34] Munts N.V., Kumkov S.S., “On the coincidence of the minimax solution and the value function in a time-optimal game with a lifeline”, Proceedings of the Steklov Institute of Mathematics, 305, suppl. 1 (2019), S125–S139 | DOI | DOI | MR | Zbl
[35] Samatov B.T., Soyibboev U.B., “Differential game with a lifeline for the inertial movements of players”, Ural Mathematical Journal, 7:2 (2021), 94–109 | DOI | MR | Zbl
[36] Alekseev V.M., Tikhomirov V.M., Fomin S.V., Optimal control, Nauka, Moscow, 1979 | MR
[37] Blagodatskikh V.I., Introduction to optimal control (linear theory), Vysshaya Shkola, Moscow, 2001