Abstract
This paper considers Pontryagin’s generalized nonstationary example [1, p. 478] with several participants under equal dynamic and inertia capabilities of the players. Multiple capture occurs when a given number of pursuers catch one evader. We obtain sufficient conditions for the multiple capture of the evader by a group of pursuers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Pontryagin, L.S., Izbrannye nauchnye trudy. Tom 2, Moscow: Nauka, 1988. Translated under the title L.S. Pontryagin: Selected Works. Vol 2, Gamkrelidze, R.V., Ed., New York: Gordon and Breach, 1986.
Chikrii, A.A., Konfliktno upravlyaemye protsessy (Conflict Controlled Processes), Kiev: Naukova Dumka, 1992.
Grigorenko, N.L., Matematicheskie metody upravleniya neskol’kimi dinamicheskimi protsessami (Mathematical Methods for Control over Several Dynamic Processes), Moscow: Mosk. Gos. Univ., 1990.
Blagodatskikh, A.I. and Petrov, N.N., Konfliktnoe vzaimodeistvie grupp upravlyaemykh obektov (Conflict Interaction of Groups of Controllable Objects), Izhevsk: Udmurt. Univ., 2009.
Pshenichnyi, B.N., Simple Pursuit by Several Objects, Kibernetika, 1976, no. 3, pp. 145–146.
Bannikov, A.S. and Petrov, N.N., On a Nonstationary Problem of Group Pursuit, Tr. Inst. Mekh. Mat., Ural. Otd. Ross. Akad. Nauk, 2010, vol. 16, no. 1, pp. 40–51.
Blagodatskikh, A.I., On a Group Pursuit Problem in Pontryagin’s Nonstationary Example, Vestn. Udmurt. Gos. Univ., Ser. Mat., 2007, no. 1, pp. 17–24.
Petrov, N.N., “Soft” Capture in Pontryagin’s Example with Many Participants, PMM J. Appl. Math. Mech., 2003, vol. 67, no. 5, pp. 671–680.
Grigorenko, N.L., A Simple Pursuit-Evasion Game for a Group of Pursuers and a Single Evader, Vestn. Mosk. Univ., Vychisl. Mat. Kibern., 1983, no. 1, pp. 41–47.
Blagodatskikh, A.I., Simultaneous Multiple Capture in a Simple Pursuit Problem, PMM J. Appl. Math. Mech., 2009, vol. 73, no. 1, pp. 36–40.
Petrov, N.N., Multiple Capture in Pontryagin’s Example with Phase Constraints, PMM J. Appl. Math. Mech., 1997, vol. 61, no. 5, pp. 725–732.
Blagodatskikh, A.I., Multiple Capture in Pontryagin’s Example, Vestn. Udmurt. Gos. Univ., Ser. Mat. Mekh. Komp. Nauki, 2009, no. 2, pp. 3–12.
Zubov, V.I., To the Theory of Recurrent Functions, Sib. Mat. Zh., 1962, vol. 3, no. 4, pp. 532–560.
Filippov, A.F., On Some Issues of Optimal Control Theory, Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., 1959, no. 6, pp. 25–32.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.N. Petrov, N.A. Solov’eva, 2016, published in Avtomatika i Telemekhanika, 2016, No. 5, pp. 128–135.
Rights and permissions
About this article
Cite this article
Petrov, N.N., Solov’eva, N.A. Multiple capture in Pontryagin’s recurrent example. Autom Remote Control 77, 855–861 (2016). https://doi.org/10.1134/S0005117916050088
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117916050088