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Possibility of encounter avoidance in a critical case. (English. Russian original) Zbl 0599.90146
Differ. Equations 20, 1451-1455 (1984); translation from Differ. Uravn. 20, No. 12, 2061-2066 (1984).
The differential game of pursuit-evasion is modelled by the p-order equation \(z^{(p)}+\sum^{p}_{i=1}a_ iz^{(p-i)}=\rho (-u+v)\), where \(z\in {\mathbb{R}}^{\nu}\), \(\nu\geq 2\), \(p\geq 1\), \(a_ i\), \(\rho \in {\mathbb{R}}^ 1\), \(\rho >0\) and u, v are pursuer and evader controls, respectively, \(v\in S\), the closed unit ball centred at \(0\in {\mathbb{R}}^{\nu}\). The game terminates if \(z(\tau)=0\) for some \(\tau\geq 0\). Sufficient conditions for avoidance of the antitarget \(z=0\) are introduced in quite general terms. It is proved that \(\nu\geq p\) and the fact that u(t) is piecewise continuous secure the avoidance.

91A24 Positional games (pursuit and evasion, etc.)
91A23 Differential games (aspects of game theory)