Abstract
We consider a linear multiperson differential game with integral constraints on the control of the players. The pursuit is assumed terminated if the solution of at least one of the equations describing the game reaches the origin at some instant of time.
In the case of one pursuer, we obtain a necessary and sufficient condition for terminating pursuit from all points of space. In the case of many pursuers, we obtain a sufficient condition for terminating pursuit from all points of space.
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REFERENCES
R. Isaacs, Differential Games, New York, 1965.
V. S. Patsko, “A differential game of quality of second order,” Prikl. Mat. Mekh. [J. Appl. Math. Mekh.], 46 (1982), no. 4.
M. S. Nikol'skii, “A direct method in linear differential games with integral constraints,” in: Controlled Systems [in Russian], vol. 2., Novosibirsk, 1969, pp. 49–59.
V. N. Ushakov, “Extremum strategies in differential games with integral constraints,” Prikl. Mat. Mekh. [J. Appl. Math. Mekh.], 36 (1972), no. 1.
N. Yu. Satimov, A. A. Khamdamov, and A. Z. Fazylov, “Differential games of multiperson pursuit with integral constraints,” Dokl. Akad. Nauk Uzbek SSR (1981), no. 10, 3–4.
N. Yu. Satimov, B. B. Rikhsiev, and G. I. Ibragimov, “On a multiperson differential game with integral constraints,” in: Topics of Current Interest in the Theory of Optimal Control and Differential Games [in Russian], Fan, Tashkent, 1996, pp. 89–94.
N. Yu. Satimov, B. B. Rikhsiev, and A. A. Khamdamov, “On a pursuit problem for multiperson linear differential and discrete games,” Mat. Sb. [Math. USSR-Sb.], 118 (1982), no. 4, 456–469.
B. B. Rikhsiev, “On a multiperson linear pursuit problem with integral constraints on the controls of the players,” in: Nonclassical Problems of Mmathematical Physics [in Russian] Fan, Tashkent, 1985, pp. 184–202.
G. I. Ibragimov, “On a multiperson optimal pursuit game against one player,” Prikl. Mat. Mekh. [J. Appl. Math. Mekh.], 62 (1998), no. 2, 199–205.
V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow, 1980, p. 496.
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Ibragimov, G.I. On a Multiperson Pursuit Problem with Integral Constraints on the Controls of the Players. Mathematical Notes 70, 181–191 (2001). https://doi.org/10.1023/A:1010250707914
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DOI: https://doi.org/10.1023/A:1010250707914