The -catch problem with two players under exponentially damping geometric constraints
The -catch problem with two players under exponentially damping geometric constraints
Abstract
Annotation. We examine the -catch and -escape problems in a differential game involving two players - a pursuer and an evader - with inertial movements. Both players are subject to exponential damping geometric constraints on their controls, meaning that the magnitudes of their acceleration vectors decrease monotonically over time. In the -catch problem, we construct an approach strategy for the pursuer, which aims to bring the pursuer within a distance of the evader (where ). We alsom define a sufficient condition for -catch. In the -escape problem, we propose a specific admissiblestrategy for the evader and identify a sufficient condition for successful evasion.
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