Abstract
The paper proposes a modified scheme of the method of resolving functions for conflict-controlled processes with a cylindrical terminal set. This scheme ensures that the game is terminated in a definite guaranteed time in the class of stroboscopic strategies without any additional conditions. The guaranteed times of various schemes of the method of resolving functions are compared with that of the first Pontryagin method in terms of convex-valued mappings for a certain structure of the terminal set.
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A. A. Chikrii, I. S. Rappoport, and K. A. Chikrii, “Multivalued mappings and their selectors in the theory of conflict-controlled processes,” Cybern. Syst. Analysis, 43, No. 5, 719–730 (2007).
A. A. Chikrii, M. V. Pittsyk, and N. B. Shishkina, “Pontryagin’s first direct method and some efficient methods of pursuit,” Cybernetics, 22, No. 5, 627–636 (1986).
A. I. Subbotin, and A. G. Chentsov, Guaranty optimization in Control Problems [in Russian], Nauka, Moscow (1981).
M. S. Nikol’skii, The First Direct Pontryagin Method in Differential Games [in Russian], Izd. MGU, Moscow (1984).
L. S. Pontryagin, Selected Scientific Works [in Russian], Vol. 2, Nauka, Moscow (1988).
A. A. Chikrii, Conflict Controlled Processes, Kluwer Acad. Publ., Boston-London-Dordrecht (1997).
N. N. Krasovskii, Game Problems on Motion Meeting [in Russian], Nauka, Moscow (1970).
Yu. G. Krivonos, I. I. Matichin, and A. A. Chikrii, Dynamic Games with Discontinuous Trajectories [in Russian], Naukova Dumka, Kyiv (2005).
B. N. Pshenichnyi and V. V. Ostapenko, Differential Games [in Russian], Naukova Dumka, Kyiv (1992).
A. A. Chikrii, “Differential games with several pursuers,” in: Trans. Banach Intern. Math. Center, Warsaw, 14, 81–107 (1985).
A. A. Chikrii, I. S. Rappoport, and K. A. Chikrii, “On pursuit theory in a class of stroboscopic strategies,” DAN Ukrainy, No. 6, 72–77 (2006).
K. A. Chikrii, “Guaranteed result for conflict-controlled processes,” Abstracts of PhD Thesis [in Russian], Kyiv (2007).
J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston-Basel-Berlin (1990).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems [in Russian], Nauka, Moscow (1974).
R. J. Aumann, “Integrals of set valued functions,” J. Math. Anal. Appl., 12, 1–12 (1965).
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 89–100, July–August 2008.
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Chikrii, A.A., Rappoport, I.S. & Chikrii, K.A. Comparison of guaranteed times in conflict-controlled motion. Cybern Syst Anal 44, 537–546 (2008). https://doi.org/10.1007/s10559-008-9024-x
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DOI: https://doi.org/10.1007/s10559-008-9024-x