Abstract
We consider Pontryagin’s generalized nonstationary example with identical dynamic and inertial capabilities of all players and with state constraints for the evaders. We derive sufficient conditions for the capture of a single evader and a given number of evaders by the pursuing group.
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References
Pontryagin, L.S., Izbrannye nauchnye trudy (Selected Scientific Papers), Moscow: Nauka, 1988, vol. II.
Chikrii, A.A., Konfliktno upravlyaemye protsessy (Conflict-Controlled Processes), Kiev, 1992.
Grigorenko, N.L., Matematicheskie metody upravleniya neskol’kimi dinamicheskimi protsessami (Mathematical Control Methods for Several Dynamic Processes), Moscow, 1990.
Blagodatskikh, A.I. and Petrov, N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh ob’ektov (Conflict Interaction of Groups of Controlled Objects), Izhevsk: Izd. Udmurt. Univ., 2009.
Blagodatskikh, A.I., On Two Oscillatory Conflict-Controlled Processes with Numerous Participants, Izv. Inst. Mat. Inform. Udmurtsk. Gos. Univ., 2005, no. 2, pp. 3–22.
Blagodatskikh, A.I., Pontryagin’s Example with Numerous Participants, Vestnik St. Petersburg Univ. Ser. 10, 2007, no. 1, pp. 16–23.
Blagodatskikh, A.I., Group Pursuit in Pontryagin’s Nonstationary Example, Differ. Uravn., 2008, vol. 44, no. 1, pp. 39–44.
Blagodatskikh, A.I., On Group Pursuit Problem in Pontryagin’s Nonstationary Example, Vestn. Udmurt. Univ. Mat., 2007, no. 1, pp. 17–24.
Blagodatskikh, A.I., On an Oscillatory Conflict-Controlled Process with Several Players, Izv. Ross. Akad. Nauk Teor. Sist. Upravl., 2005, no. 5, pp. 43–45.
Petrov, N.N. and Shuravina, I.N., On “Soft” Capture in a Group Pursuit Problem, Izv. Ross. Akad. Nauk Teor. Sist. Upravl., 2009, no. 4, pp. 24–28.
Petrov, N.N., Pontryagin’s Nonstationary Example with State Constraints, Problemy Upravlen. Inform., 2000, no. 4, pp. 18–24.
Petrov, N.N., Multiple Capture in the Pontryagin Example with State Constraints, Prikl. Mat. Mekh., 1997, vol. 61, no. 5, pp. 747–754.
Petrov, N.N., “Soft” Capture in an Example of L.S. Pontryagin with Several Participants, Prikl. Mat. Mekh., 2003, vol. 67, no. 5, pp. 759–770.
Bannikov, A.S. and Petrov, N.N., A Remark on the Nonstationary Problem of Group Pursuit, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2010, vol. 16, no. 1, pp. 40–51.
Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability), Moscow: Nauka, 1967.
Petrov, N.N., Controllability of Autonomous Systems, Differ. Uravn., 1968, vol. 4, no. 4, pp. 606–617.
Hall, M.J., Combinatorial Theory, Walham-Toronto-London: Blaidell Publ., 1967. Translated under the title Kombinatorika, Moscow: Mir, 1970.
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Original Russian Text © A.I. Blagodatskikh, N.N. Petrov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 3, pp. 387–394.
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Blagodatskikh, A.I., Petrov, N.N. Group pursuit with state constraints in Pontryagin’s almost periodic example. Diff Equat 51, 391–398 (2015). https://doi.org/10.1134/S001226611503009X
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DOI: https://doi.org/10.1134/S001226611503009X