Possibility of encounter avoidance in a critical case. (English. Russian original) Zbl 0599.90146

Satimov, N.

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.

MSC:

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

Keywords:

Sufficient conditions for avoidance