O‘zbekiston matematika jurnali Volume 69 Issue 4 (2025) · pp. 201-216
Differential game with a ``life-line'' for nonlinear motion dynamics of players
Turgunboeva, M.A., Soyibboev, U.B.
Abstract
We investigate the interception problem in a differential game with non-inertial players (a pursuer and an evader) who move in dynamic flow fields with various influences. Throughout the paper, we solve the pursuit and ``life-line'' game problems. To solve the pursuit, the strategy of parallel pursuit ($\bf{\Pi}$-strategy for short) is defined and used. With the help of the $\bf{\Pi}$-strategy and applying the Gr\"{o}nwall-Bellman inequality, sufficient pursuit condition is determined. In order to solve the ``life-line'' game to the advantage of the pursuer, we build the set of meeting points of the players and prove that this set monotonically decreases with regard to inclusion relative to time. The ``life-line'' game to the advantage of the evader is solved by constructing evader's attainability domain where it reaches without being caught for an arbitrary control of the pursuer.
Differential game, Caratheodory's conditions, Lipschitz's condition, players, geometric constraint, pursuit, ``life-line'', $\bf{\Pi}$-strategy, Gr\
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