Pursuit differential game with high-order dynamic

Abstract

This study examines a pursuit–evasion differential game with finitely many pursuers and a single evader moving inside a nonempty compact convex region of $\mathbb{R}^{2}$ The dynamics of all participants are governed by ordinary differential equations of degrees $n$ and $m$, while their control inputs satisfy coordinate-wise integral constraints. Capture is said to occur when at least one pursuer reaches the same position as the evader. Sufficient conditions ensuring that the pursuers can guarantee capture are derived, and constructive strategies are proposed to realize this outcome.