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On the evadable sets of differential evasion games. (English) Zbl 0651.90108
The author considers an autonomous differential game described by the equation $$\dot z=f(z,u,v)$$, $$z(0)=z_ 0$$, $$u\in U\in comp R^ p$$, $$v\in V\in compR^ q$$. Here $$z\in R^ n$$, u is the pursuit control, v is the evasion control. The terminal set of the game is a linear subspace M of $$R^ n$$ with dim $$M\leq n-2$$. Player P chooses his control $$u(\cdot)=(u(t)$$, $$0\leq t<\infty)$$ in the class $${\mathcal U}_ h[0,\infty)$$ defined as follows: $${\mathcal U}_ h[0,\infty):=\{u:$$ [0,$$\infty)\to U$$, u is measurable; $$\forall \delta \in [0,\infty)$$ $$\| u(t)-u(t- \delta)\| \leq h(\delta)$$ a.e. $$t\in [\delta,\infty)\}$$ where h: [0,$$\infty)\to [0,\infty)$$ is a nondecreasing function, $$h(0)=0$$. Player E forms his strategy $$S_{\delta}$$ having complete information about $$z(\cdot)=(z(s)$$, $$0\leq s\leq t-\delta)$$ and $$u(\cdot)=(u(s)$$, $$0\leq s\leq t-\delta)$$ where the parameter $$\delta >0$$ describes an information delay.
The purpose of the paper is to discuss the evasion game with the mentioned information delay and to get some sufficient conditions for evadability and strict evadability. The results of the paper extend the results obtained earlier by L. S. Pontryagin, N. Satimov, B. N. Pshenichnyj and other authors.
Reviewer: A.Kleimenov

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