On a nonstationary problem of group pursuit
Tóm tắt
Pontryagin’s classical nonstationary example with many participants and phase constraints on the evader’s states with equal dynamic and inertia capabilities of the players is considered. The case of a simple motion is considered separately. Solvability conditions for problems of pursuit and evasion are obtained.
Tài liệu tham khảo
L. S. Pontryagin, Selected Scientific Works (Nauka, Moscow, 1988), Vol. 2 [in Russian].
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974; Springer-Verlag, Berlin, 1988).
A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems (Nauka, Moscow, 1981) [in Russian].
A. A. Chikrii, Conflict Controlled Processes (Naukova Dumka, Kiev, 1992; Kluwer Acad., Boston, 1997).
N. L. Grigorenko, Mathematical Methods of Controlling Several Dynamic Processes (Izd. Mosk. Gos. Univ., Moscow, 1990) [in Russian].
A. I. Blagodatskikh and N. N. Petrov, Conflict Interaction of Groups of Controlled Objects (Izd. Udmurtsk. Univ., Izhevsk, 2009) [in Russian].
B. N. Pshenichnyi, Kibernetika 3, 145 (1976).
N. L. Grigorenko, Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibernet. 1, 41 (1983).
R. P. Ivanov, Dokl. Akad. Nauk SSSR 254(6), 1318 (1980).
N. N. Petrov, Game Theory (Izd. Udmurtsk. Univ., Izhevsk, 1997) [in Russian].
N. N. Petrov, Avtomat. i Telemekh. 5, 22 (1992).
A. S. Bannikov, Vestn. Udmurtsk. Univ., Ser. Mat. Mekh. Komp. Nauki 3, 3 (2009).
A. V. Mezentsev, Izv. Akad. Nauk SSSR, Ser. Tekhn. Kibernet. 6, 3 (1971).
M. S. Nikol’skii, Kibernetika 6, 98 (1970).
T. Parthasarathy and T. Raghavan, Some Topics in Two-Person Games (Elsevier, New York, 1971; Moscow, Mir, 1974).
N. N. Petrov, Differents. Uravneniya 4(4), 606 (1968).