Abstract:
Sufficient conditions of pursuit termination are proposed for a linear differential game of pursuit when one of the players applies an impulse-type control and the other player applies an integrally constrained control. Methods for finding the pursuer's controls that guarantee the termination of pursuit in a finite time are presented. At the end of the paper, we give examples illustrating the results. The method used in the second example provides an alternative: the space Rm is divided into two parts so that the pursuit can be terminated from any point of the first part and the pursuit cannot be terminated from any point of the second part.
Citation:
M. Tukhtasinov, “A linear differential game of pursuit with impulse and integrally constrained controls of the players”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 3, 2016, 273–282
\Bibitem{Tuk16}
\by M.~Tukhtasinov
\paper A linear differential game of pursuit with impulse and integrally constrained controls of the players
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 3
\pages 273--282
\mathnet{http://mi.mathnet.ru/timm1344}
\crossref{https://doi.org/10.21538/0134-4889-2016-22-3-273-282}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3555733}
\elib{https://elibrary.ru/item.asp?id=26530903}
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This publication is cited in the following 12 articles:
A. I. Machtakova, N. N. Petrov, “O dvukh zadachakh presledovaniya gruppy ubegayuschikh v differentsialnykh igrakh s drobnymi proizvodnymi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:1 (2024), 65–79
Numanzhon A. Mamadaliev, Khamdam Ya. Mustapokulov, Mukhammadsodik M. Abdumannopov, “Differentsialnye igry presledovaniya neitralnogo tipa s integralnymi ogranicheniyami na upravleniya igrokov”, MTIP, 16:4 (2024), 45–68
N. A. Mamadaliev, Kh. Ya. Mustapokulov, G. M. Abdualimova, “Metod razreshayuschikh funktsii dlya resheniya zadachi presledovaniya s integralnymi ogranicheniyami na upravleniya igrokov”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:1 (2023), 103–118
I. V. Izmestev, V. I. Ukhobotov, “Odnotipnaya zadacha impulsnogo presledovaniya ob'ekta s izmenyayuscheisya dinamikoi”, Chelyab. fiz.-matem. zhurn., 8:4 (2023), 502–515
G. M. Abdualimova, N. A. Mamadaliev, M. Tukhtasinov, “Sufficient solvability conditions for the problem of pursuit under an impulse action”, Comput. Math. Math. Phys., 63:7 (2023), 1166–1175
N. A. Mamadaliev, B. Kh. Khayitkulov, “Complete solution of a class of differential pursuit games with integral constraint and impulse control”, Russian Math. (Iz. VUZ), 66:3 (2022), 22–29
I. V. Izmestev, V. I. Ukhobotov, “Minimizatsiya zapasa resursov v odnoi impulsnoi differentsialnoi igre s nevypuklym terminalnym mnozhestvom”, Chelyab. fiz.-matem. zhurn., 6:1 (2021), 22–33
N. A. Mamadaliev, T. T. Ibaydullaev, “On the modified third method in the pursuit problem for differential-difference equations of neutral type”, Russian Math. (Iz. VUZ), 65:11 (2021), 18–28
Igor' V. Izmest'ev, Lecture Notes in Control and Information Sciences - Proceedings, Stability, Control and Differential Games, 2020, 345
M. Tukhtasinov, Kh. Ya. Mustapokulov, “$\varepsilon$-pozitsionnye strategii v teorii differentsialnykh igr presledovaniya i ob invariantnosti postoyannogo mnogoznachnogo otobrazheniya v zadache teploprovodnosti”, Sovremennye problemy matematiki i fiziki, SMFN, 65, no. 1, Rossiiskii universitet druzhby narodov, M., 2019, 124–136
V. I. Ukhobotov, I. V. Izmestyev, “Impulse differential game with a mixed constraint on the choice of the control of the first player”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S161–S174
I. V. Izmest'ev, V. I. Ukhobotov, “Game problem of convergence of a group of objects with different types of dynamic and target”, 2018 Global Smart Industry Conference (GloSIC), IEEE, 2018
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