Interception Conditions in Multi-Agent Pursuit Games Governed by Linear Dynamics with Gronwall-type Constraints

This paper investigates a multi-agent pursuit problem in which a group of pursuers seeks to intercept one or more evaders within a fixed operational time horizon. The motion of both pursuers and evaders is described by first-order linear differential equations, and the control inputs available to the agents are subject to Gronwall-type constraints. Pursuit is considered successful when at least one pursuer reaches the position of each evader at a finite time within the prescribed duration. Within this framework, we construct permissible strategies for the pursuers and derive sufficient conditions under which interception is guaranteed despite the evaders’ counteractions. To support the theoretical results, we present numerical examples that demonstrate the effectiveness of the proposed strategies and confirm the analytical conditions for successful pursuit.