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A pursuit problem in many person differential games. (Russian) Zbl 0662.90107
A general differential game for m pursuers and two evadors is described (the problem formulation follows L. S. Pontryagin); pursuers’ strategies have the form $$u_ i(t)=V_ i(t,v_ 1(t),v_ 2(t))$$ where $$v_ 1(t)$$ and $$v_ 2(t)$$ are controls of the evadors. Capture of the j-th evador at time $$t_ j$$ implies $$z_{ij}(t_ j)\in M_{ij}(t_ j)$$ for some $$i\leq m$$; here $$z_{ij}$$ is a state of a system describing the interaction process for the i-th pursuer and the j-th evador, $$M_{ij}(t)=M^ 1_{ij}+M^ 2_{ij}(t)$$, $$M^ 1_{ij}$$ are linear subspaces, $$M^ 2_{ij}(t)$$ are convex compact functions continuous in t. System equations linear in $$z_{ij}$$ are considered. Sufficient algebraic conditions for two evadors to be captured within a finite time interval are given, and an upper bound for the capture time is deduced. For the case of three pursuers $$\dot x{}_ i=u_ i(t)$$, $$\| u_ i(t)\| \leq 1$$, and two evadors $$\dot y{}_ j=v_ j(t)$$, $$\| v_ j(t)\| \leq 1$$, it is shown that for any initial position three situations are possible: (a) ensured evasion, (b) capture of one evador, (c) capture of one prescribed evador.
Reviewer: A.V.Kryazhimskij

##### MSC:
 91A24 Positional games (pursuit and evasion, etc.) 91A23 Differential games (aspects of game theory) 91A99 Game theory
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