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Section
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Mathematics
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Title
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Multiple capture of rigidly coordinated evaders
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Author(-s)
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Blagodatskikh A.I.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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capture, multiple capture, simultaneous multiple capture, pursuit, evasion, differential games, conflict-controlled processes
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UDC
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517.977.8, 519.837.4
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MSC
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49N70, 49N75
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DOI
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10.20537/vm160104
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Received
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20 February 2016
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Language
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Russian
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Citation
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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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References
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