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Russia Izhevsk
Section Mathematics
Title Multiple capture of rigidly coordinated evaders
Author(-s) Blagodatskikh A.I.a
Affiliations Udmurt State Universitya
Abstract The present paper deals with the problem of pursuit of a group of rigidly coordinated evaders in a nonstationary conflict-controlled process with equal opportunities $$\begin{array}{llllllllcccc} P_i & : & \dot x_i = A(t)x_i + u_i,& u_i \in U(t), & x_i(t_0) = X_i^0, & i = 1,2, \dots, n, \\ E_j & : & \dot y_j = A(t)y_j + v, & v \in U(t) , & y_j(t_0) = Y_j^0 , & j = 1,2, \dots, m. \\ \end{array}$$ We say that a multiple capture in the problem of pursuit holds if the specified number of pursuers catch evaders, possibly at different times $$x_\alpha (\tau_\alpha) = y_{j_\alpha}(\tau_\alpha), \quad \alpha \in \Lambda, \quad \Lambda \subset \{1,2, \dots, n\}, \quad |\Lambda| = b\quad (n \geqslant b \geqslant 1), \quad j_\alpha \subset \{1,2, \dots, m\}.$$ The problem of nonstrict simultaneous multiple capture requires that capture moments coincide $$x_\alpha (\tau) = y_{j_\alpha}(\tau), \quad \alpha \in \Lambda.$$ The problem of a simultaneous multiple capture requires that lowest capture moments coincide $$x_\alpha (\tau) = y_{j_\alpha}(\tau), \quad x_\alpha(s) \ne y_{j_\alpha}(s), \quad s \in [t_0, \tau), \quad \alpha \in \Lambda.$$ In this paper we obtain necessary and sufficient conditions for simultaneous multiple capture and nonstrict simultaneous multiple capture.
Keywords capture, multiple capture, simultaneous multiple capture, pursuit, evasion, differential games, conflict-controlled processes
UDC 517.977.8, 519.837.4
MSC 49N70, 49N75
DOI 10.20537/vm160104
Received 20 February 2016
Language Russian
Citation Blagodatskikh A.I. Multiple capture of rigidly coordinated evaders, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 46-57.
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